diff --git a/SRC/zhetf2_rk.f b/SRC/zhetf2_rk.f
index fe737e631b..050c7993d0 100644
--- a/SRC/zhetf2_rk.f
+++ b/SRC/zhetf2_rk.f
@@ -417,7 +417,7 @@ SUBROUTINE ZHETF2_RK( UPLO, N, A, LDA, E, IPIV, INFO )
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
@@ -770,7 +770,7 @@ SUBROUTINE ZHETF2_RK( UPLO, N, A, LDA, E, IPIV, INFO )
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
diff --git a/SRC/zhetf2_rook.f b/SRC/zhetf2_rook.f
index f9fd900c34..94bb297367 100644
--- a/SRC/zhetf2_rook.f
+++ b/SRC/zhetf2_rook.f
@@ -357,7 +357,7 @@ SUBROUTINE ZHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
@@ -669,7 +669,7 @@ SUBROUTINE ZHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
diff --git a/SRC/zlahef_rk.f b/SRC/zlahef_rk.f
index 901fb25a4b..ed66e133da 100644
--- a/SRC/zlahef_rk.f
+++ b/SRC/zlahef_rk.f
@@ -460,7 +460,7 @@ SUBROUTINE ZLAHEF_RK( UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW,
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( W( IMAX,KW-1 ) ) )
@@ -599,7 +599,7 @@ SUBROUTINE ZLAHEF_RK( UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW,
 *                 A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k)
 *
 *              (NOTE: No need to use for Hermitian matrix
-*              A( K, K ) = REAL( W( K, K) ) to separately copy diagonal
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
 *              element D(k,k) from W (potentially saves only one load))
                CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
                IF( K.GT.1 ) THEN
@@ -912,7 +912,7 @@ SUBROUTINE ZLAHEF_RK( UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW,
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,K+1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,K+1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( W( IMAX,K+1 ) ) )
@@ -1042,7 +1042,7 @@ SUBROUTINE ZLAHEF_RK( UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW,
 *                 A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k)
 *
 *              (NOTE: No need to use for Hermitian matrix
-*              A( K, K ) = REAL( W( K, K) ) to separately copy diagonal
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
 *              element D(k,k) from W (potentially saves only one load))
                CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
                IF( K.LT.N ) THEN
diff --git a/SRC/zlahef_rook.f b/SRC/zlahef_rook.f
index 6905a95db4..65f70a5978 100644
--- a/SRC/zlahef_rook.f
+++ b/SRC/zlahef_rook.f
@@ -370,7 +370,7 @@ SUBROUTINE ZLAHEF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( W( IMAX,KW-1 ) ) )
@@ -509,7 +509,7 @@ SUBROUTINE ZLAHEF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
 *                 A(1:k-1,k) := U(1:k-1,k) = W(1:k-1,kw)/D(k,k)
 *
 *              (NOTE: No need to use for Hermitian matrix
-*              A( K, K ) = REAL( W( K, K) ) to separately copy diagonal
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
 *              element D(k,k) from W (potentially saves only one load))
                CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
                IF( K.GT.1 ) THEN
@@ -833,7 +833,7 @@ SUBROUTINE ZLAHEF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
 *
 *                 Case(2)
 *                 Equivalent to testing for
-*                 ABS( REAL( W( IMAX,K+1 ) ) ).GE.ALPHA*ROWMAX
+*                 ABS( DBLE( W( IMAX,K+1 ) ) ).GE.ALPHA*ROWMAX
 *                 (used to handle NaN and Inf)
 *
                   IF( .NOT.( ABS( DBLE( W( IMAX,K+1 ) ) )
@@ -963,7 +963,7 @@ SUBROUTINE ZLAHEF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
 *                 A(k+1:N,k) := L(k+1:N,k) = W(k+1:N,k)/D(k,k)
 *
 *              (NOTE: No need to use for Hermitian matrix
-*              A( K, K ) = REAL( W( K, K) ) to separately copy diagonal
+*              A( K, K ) = DBLE( W( K, K) ) to separately copy diagonal
 *              element D(k,k) from W (potentially saves only one load))
                CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
                IF( K.LT.N ) THEN
diff --git a/SRC/ztrevc3.f b/SRC/ztrevc3.f
index 93c833e62a..6300e80aec 100644
--- a/SRC/ztrevc3.f
+++ b/SRC/ztrevc3.f
@@ -286,13 +286,13 @@ SUBROUTINE ZTREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
      $                   ZGEMM, DLABAD, ZLASET, ZLACPY
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          ABS, DBLE, DCMPLX, CONJG, AIMAG, MAX
+      INTRINSIC          ABS, DBLE, DCMPLX, CONJG, DIMAG, MAX
 *     ..
 *     .. Statement Functions ..
       DOUBLE PRECISION   CABS1
 *     ..
 *     .. Statement Function definitions ..
-      CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( AIMAG( CDUM ) )
+      CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
 *     ..
 *     .. Executable Statements ..
 *
diff --git a/TESTING/EIG/cbdt01.f b/TESTING/EIG/cbdt01.f
index edcbcbb39f..f5633bdc31 100644
--- a/TESTING/EIG/cbdt01.f
+++ b/TESTING/EIG/cbdt01.f
@@ -28,13 +28,13 @@
 *> \verbatim
 *>
 *> CBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary
+*>    A = Q * B * P**H
+*> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -49,7 +49,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**H.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -78,7 +78,7 @@
 *> \verbatim
 *>          Q is COMPLEX array, dimension (LDQ,N)
 *>          The m by min(m,n) unitary matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -103,8 +103,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is COMPLEX array, dimension (LDPT,N)
-*>          The min(m,n) by n unitary matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n unitary matrix P**H in the reduction
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -127,7 +127,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -187,7 +188,7 @@ SUBROUTINE CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**H one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -265,7 +266,7 @@ SUBROUTINE CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *
       ANORM = CLANGE( '1', M, N, A, LDA, RWORK )
       EPS = SLAMCH( 'Precision' )
diff --git a/TESTING/EIG/cbdt02.f b/TESTING/EIG/cbdt02.f
index 87fda4a71d..6ef39a96b3 100644
--- a/TESTING/EIG/cbdt02.f
+++ b/TESTING/EIG/cbdt02.f
@@ -27,9 +27,10 @@
 *>
 *> \verbatim
 *>
-*> CBDT02 tests the change of basis C = U' * B by computing the residual
+*> CBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
-*>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>    RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *>
 *> where B and C are M by N matrices, U is an M by M orthogonal matrix,
 *> and EPS is the machine precision.
@@ -66,7 +67,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is COMPLEX array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC
@@ -100,7 +101,7 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>          RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *> \endverbatim
 *
 *  Authors:
@@ -161,7 +162,7 @@ SUBROUTINE CBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
       REALMN = REAL( MAX( M, N ) )
       EPS = SLAMCH( 'Precision' )
 *
-*     Compute norm( B - U * C )
+*     Compute norm(B - U * C)
 *
       DO 10 J = 1, N
          CALL CCOPY( M, B( 1, J ), 1, WORK, 1 )
diff --git a/TESTING/EIG/clarhs.f b/TESTING/EIG/clarhs.f
index e1d7ebdddc..9842df9599 100644
--- a/TESTING/EIG/clarhs.f
+++ b/TESTING/EIG/clarhs.f
@@ -29,9 +29,8 @@
 *>
 *> CLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
-*> transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A, A**T or A**H, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -85,9 +84,9 @@
 *>          TRANS is CHARACTER*1
 *>          Used only if A is nonsymmetric; specifies the operation
 *>          applied to the matrix A.
-*>          = 'N':  B := A    * X
-*>          = 'T':  B := A**T * X
-*>          = 'C':  B := A**H * X
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -313,7 +312,7 @@ SUBROUTINE CLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/EIG/dbdt01.f b/TESTING/EIG/dbdt01.f
index 40ac373ba8..69e0b5ffc2 100644
--- a/TESTING/EIG/dbdt01.f
+++ b/TESTING/EIG/dbdt01.f
@@ -27,13 +27,13 @@
 *> \verbatim
 *>
 *> DBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
+*>    A = Q * B * P**T
+*> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -48,7 +48,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**T.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -77,7 +77,7 @@
 *> \verbatim
 *>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
 *>          The m by min(m,n) orthogonal matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -102,8 +102,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is DOUBLE PRECISION array, dimension (LDPT,N)
-*>          The min(m,n) by n orthogonal matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n orthogonal matrix P**T in the reduction
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -121,7 +121,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -180,7 +181,7 @@ SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**T one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -258,7 +259,7 @@ SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *
       ANORM = DLANGE( '1', M, N, A, LDA, WORK )
       EPS = DLAMCH( 'Precision' )
diff --git a/TESTING/EIG/dbdt02.f b/TESTING/EIG/dbdt02.f
index fd1b030e0c..ac0291219b 100644
--- a/TESTING/EIG/dbdt02.f
+++ b/TESTING/EIG/dbdt02.f
@@ -25,9 +25,10 @@
 *>
 *> \verbatim
 *>
-*> DBDT02 tests the change of basis C = U' * B by computing the residual
+*> DBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
-*>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>    RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *>
 *> where B and C are M by N matrices, U is an M by M orthogonal matrix,
 *> and EPS is the machine precision.
@@ -64,7 +65,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is DOUBLE PRECISION array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC
@@ -93,7 +94,7 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>          RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *> \endverbatim
 *
 *  Authors:
@@ -152,7 +153,7 @@ SUBROUTINE DBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
       REALMN = DBLE( MAX( M, N ) )
       EPS = DLAMCH( 'Precision' )
 *
-*     Compute norm( B - U * C )
+*     Compute norm(B - U * C)
 *
       DO 10 J = 1, N
          CALL DCOPY( M, B( 1, J ), 1, WORK, 1 )
diff --git a/TESTING/EIG/dlarhs.f b/TESTING/EIG/dlarhs.f
index 2505ae227b..bc048bbcfe 100644
--- a/TESTING/EIG/dlarhs.f
+++ b/TESTING/EIG/dlarhs.f
@@ -29,8 +29,8 @@
 *>
 *> DLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -79,10 +79,11 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          Specifies the operation applied to the matrix A.
-*>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          Used only if A is nonsymmetric; specifies the operation
+*>          applied to the matrix A.
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -305,7 +306,7 @@ SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/EIG/sbdt01.f b/TESTING/EIG/sbdt01.f
index 2e4e48df33..fdc30a51ea 100644
--- a/TESTING/EIG/sbdt01.f
+++ b/TESTING/EIG/sbdt01.f
@@ -27,13 +27,13 @@
 *> \verbatim
 *>
 *> SBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
+*>    A = Q * B * P**T
+*> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -48,7 +48,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**T.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -77,7 +77,7 @@
 *> \verbatim
 *>          Q is REAL array, dimension (LDQ,N)
 *>          The m by min(m,n) orthogonal matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -102,8 +102,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is REAL array, dimension (LDPT,N)
-*>          The min(m,n) by n orthogonal matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n orthogonal matrix P**T in the reduction
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -121,7 +121,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -180,7 +181,7 @@ SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**T one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -258,7 +259,7 @@ SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *
       ANORM = SLANGE( '1', M, N, A, LDA, WORK )
       EPS = SLAMCH( 'Precision' )
diff --git a/TESTING/EIG/sbdt02.f b/TESTING/EIG/sbdt02.f
index cbce82ba7c..e86863f78b 100644
--- a/TESTING/EIG/sbdt02.f
+++ b/TESTING/EIG/sbdt02.f
@@ -25,9 +25,10 @@
 *>
 *> \verbatim
 *>
-*> SBDT02 tests the change of basis C = U' * B by computing the residual
+*> SBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
-*>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>    RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *>
 *> where B and C are M by N matrices, U is an M by M orthogonal matrix,
 *> and EPS is the machine precision.
@@ -64,7 +65,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is REAL array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC
@@ -93,7 +94,7 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>          RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *> \endverbatim
 *
 *  Authors:
@@ -152,7 +153,7 @@ SUBROUTINE SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
       REALMN = REAL( MAX( M, N ) )
       EPS = SLAMCH( 'Precision' )
 *
-*     Compute norm( B - U * C )
+*     Compute norm(B - U * C)
 *
       DO 10 J = 1, N
          CALL SCOPY( M, B( 1, J ), 1, WORK, 1 )
diff --git a/TESTING/EIG/slarhs.f b/TESTING/EIG/slarhs.f
index 0d736f3505..bdb74724e8 100644
--- a/TESTING/EIG/slarhs.f
+++ b/TESTING/EIG/slarhs.f
@@ -29,8 +29,8 @@
 *>
 *> SLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -79,10 +79,11 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          Specifies the operation applied to the matrix A.
-*>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          Used only if A is nonsymmetric; specifies the operation
+*>          applied to the matrix A.
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -305,7 +306,7 @@ SUBROUTINE SLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/EIG/zbdt01.f b/TESTING/EIG/zbdt01.f
index 78d771f198..afe2fa89a5 100644
--- a/TESTING/EIG/zbdt01.f
+++ b/TESTING/EIG/zbdt01.f
@@ -28,13 +28,13 @@
 *> \verbatim
 *>
 *> ZBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary
+*>    A = Q * B * P**H
+*> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -49,7 +49,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**H.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -78,7 +78,7 @@
 *> \verbatim
 *>          Q is COMPLEX*16 array, dimension (LDQ,N)
 *>          The m by min(m,n) unitary matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -103,8 +103,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is COMPLEX*16 array, dimension (LDPT,N)
-*>          The min(m,n) by n unitary matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n unitary matrix P**H in the reduction
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -127,7 +127,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -187,7 +188,7 @@ SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**H one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -265,7 +266,7 @@ SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *
       ANORM = ZLANGE( '1', M, N, A, LDA, RWORK )
       EPS = DLAMCH( 'Precision' )
diff --git a/TESTING/EIG/zbdt02.f b/TESTING/EIG/zbdt02.f
index 72fa78a37f..f0da37222b 100644
--- a/TESTING/EIG/zbdt02.f
+++ b/TESTING/EIG/zbdt02.f
@@ -27,9 +27,10 @@
 *>
 *> \verbatim
 *>
-*> ZBDT02 tests the change of basis C = U' * B by computing the residual
+*> ZBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
-*>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>    RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *>
 *> where B and C are M by N matrices, U is an M by M orthogonal matrix,
 *> and EPS is the machine precision.
@@ -66,7 +67,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is COMPLEX*16 array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC
@@ -100,7 +101,7 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
+*>          RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
 *> \endverbatim
 *
 *  Authors:
@@ -161,7 +162,7 @@ SUBROUTINE ZBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK,
       REALMN = DBLE( MAX( M, N ) )
       EPS = DLAMCH( 'Precision' )
 *
-*     Compute norm( B - U * C )
+*     Compute norm(B - U * C)
 *
       DO 10 J = 1, N
          CALL ZCOPY( M, B( 1, J ), 1, WORK, 1 )
diff --git a/TESTING/EIG/zlarhs.f b/TESTING/EIG/zlarhs.f
index e3107f231e..1dc003f2e4 100644
--- a/TESTING/EIG/zlarhs.f
+++ b/TESTING/EIG/zlarhs.f
@@ -29,9 +29,8 @@
 *>
 *> ZLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
-*> transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A, A**T, or A**H, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -85,9 +84,9 @@
 *>          TRANS is CHARACTER*1
 *>          Used only if A is nonsymmetric; specifies the operation
 *>          applied to the matrix A.
-*>          = 'N':  B := A    * X
-*>          = 'T':  B := A**T * X
-*>          = 'C':  B := A**H * X
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -313,7 +312,7 @@ SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/LIN/cchkge.f b/TESTING/LIN/cchkge.f
index d970571ac3..0ee1c85c57 100644
--- a/TESTING/LIN/cchkge.f
+++ b/TESTING/LIN/cchkge.f
@@ -78,7 +78,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkhe.f b/TESTING/LIN/cchkhe.f
index 875d8e3997..1ff0257579 100644
--- a/TESTING/LIN/cchkhe.f
+++ b/TESTING/LIN/cchkhe.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkhe_aa.f b/TESTING/LIN/cchkhe_aa.f
index 826faf7d42..487f9941e8 100644
--- a/TESTING/LIN/cchkhe_aa.f
+++ b/TESTING/LIN/cchkhe_aa.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkhe_aa_2stage.f b/TESTING/LIN/cchkhe_aa_2stage.f
index 6ba9c309ca..30a61261f5 100644
--- a/TESTING/LIN/cchkhe_aa_2stage.f
+++ b/TESTING/LIN/cchkhe_aa_2stage.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkhe_rk.f b/TESTING/LIN/cchkhe_rk.f
index 96a2fe1d69..4f9801f88d 100644
--- a/TESTING/LIN/cchkhe_rk.f
+++ b/TESTING/LIN/cchkhe_rk.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkhe_rook.f b/TESTING/LIN/cchkhe_rook.f
index 52ab5db702..72a4a1d4d0 100644
--- a/TESTING/LIN/cchkhe_rook.f
+++ b/TESTING/LIN/cchkhe_rook.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchklqt.f b/TESTING/LIN/cchklqt.f
index 57b843fbc0..7ec8b2c622 100644
--- a/TESTING/LIN/cchklqt.f
+++ b/TESTING/LIN/cchklqt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchklqtp.f b/TESTING/LIN/cchklqtp.f
index 9fd21a964b..987c0c3654 100644
--- a/TESTING/LIN/cchklqtp.f
+++ b/TESTING/LIN/cchklqtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkpb.f b/TESTING/LIN/cchkpb.f
index bcfc771f77..4d1ab6f4f9 100644
--- a/TESTING/LIN/cchkpb.f
+++ b/TESTING/LIN/cchkpb.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkpo.f b/TESTING/LIN/cchkpo.f
index 87d885bf26..8cf85bf6e4 100644
--- a/TESTING/LIN/cchkpo.f
+++ b/TESTING/LIN/cchkpo.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkps.f b/TESTING/LIN/cchkps.f
index 45702fa692..d77ffc0262 100644
--- a/TESTING/LIN/cchkps.f
+++ b/TESTING/LIN/cchkps.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the block size NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkqrt.f b/TESTING/LIN/cchkqrt.f
index 5dc69dd034..7aeb6df4be 100644
--- a/TESTING/LIN/cchkqrt.f
+++ b/TESTING/LIN/cchkqrt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkqrtp.f b/TESTING/LIN/cchkqrtp.f
index 246e761215..6820c90042 100644
--- a/TESTING/LIN/cchkqrtp.f
+++ b/TESTING/LIN/cchkqrtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchksy.f b/TESTING/LIN/cchksy.f
index 3392188237..c933f0c967 100644
--- a/TESTING/LIN/cchksy.f
+++ b/TESTING/LIN/cchksy.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchksy_aa.f b/TESTING/LIN/cchksy_aa.f
index 735e79bd04..015d5a68e6 100644
--- a/TESTING/LIN/cchksy_aa.f
+++ b/TESTING/LIN/cchksy_aa.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchksy_aa_2stage.f b/TESTING/LIN/cchksy_aa_2stage.f
index 7a0dcc5673..bede7cca5e 100644
--- a/TESTING/LIN/cchksy_aa_2stage.f
+++ b/TESTING/LIN/cchksy_aa_2stage.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchksy_rk.f b/TESTING/LIN/cchksy_rk.f
index 9ba653c093..f4954054f4 100644
--- a/TESTING/LIN/cchksy_rk.f
+++ b/TESTING/LIN/cchksy_rk.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchksy_rook.f b/TESTING/LIN/cchksy_rook.f
index bbe18ebf9c..2031089801 100644
--- a/TESTING/LIN/cchksy_rook.f
+++ b/TESTING/LIN/cchksy_rook.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchktsqr.f b/TESTING/LIN/cchktsqr.f
index e71656671a..0a85d7cf1e 100644
--- a/TESTING/LIN/cchktsqr.f
+++ b/TESTING/LIN/cchktsqr.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cchkunhr_col.f b/TESTING/LIN/cchkunhr_col.f
index 0d6a9063db..b2f233e258 100644
--- a/TESTING/LIN/cchkunhr_col.f
+++ b/TESTING/LIN/cchkunhr_col.f
@@ -82,7 +82,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/cgbt01.f b/TESTING/LIN/cgbt01.f
index 277b0b1ab8..148076e9ac 100644
--- a/TESTING/LIN/cgbt01.f
+++ b/TESTING/LIN/cgbt01.f
@@ -26,7 +26,7 @@
 *>
 *> \verbatim
 *>
-*> CGBT01 reconstructs a band matrix  A  from its L*U factorization and
+*> CGBT01 reconstructs a band matrix A from its L*U factorization and
 *> computes the residual:
 *>    norm(L*U - A) / ( N * norm(A) * EPS ),
 *> where EPS is the machine epsilon.
@@ -226,7 +226,7 @@ SUBROUTINE CGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
          END IF
    40 CONTINUE
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       IF( ANORM.LE.ZERO ) THEN
          IF( RESID.NE.ZERO )
diff --git a/TESTING/LIN/cgbt02.f b/TESTING/LIN/cgbt02.f
index 8c51e8b2a2..3204a89867 100644
--- a/TESTING/LIN/cgbt02.f
+++ b/TESTING/LIN/cgbt02.f
@@ -31,7 +31,7 @@
 *> equations op(A)*X = B:
 *>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 *> where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
-*> machine precision.
+*> machine epsilon.
 *> \endverbatim
 *
 *  Arguments:
diff --git a/TESTING/LIN/cgbt05.f b/TESTING/LIN/cgbt05.f
index 859f8b3eb2..34b81058fd 100644
--- a/TESTING/LIN/cgbt05.f
+++ b/TESTING/LIN/cgbt05.f
@@ -30,7 +30,7 @@
 *> CGBT05 tests the error bounds from iterative refinement for the
 *> computed solution to a system of equations op(A)*X = B, where A is a
 *> general band matrix of order n with kl subdiagonals and ku
-*> superdiagonals and op(A) = A or A**T, depending on TRANS.
+*> superdiagonals and op(A) = A, A**T, or A**H, depending on TRANS.
 *>
 *> RESLTS(1) = test of the error bound
 *>           = norm(X - XACT) / ( norm(X) * FERR )
@@ -50,7 +50,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the form of the system of equations.
-*>          = 'N':  A * X = B     (No transpose)
+*>          = 'N':  A    * X = B  (No transpose)
 *>          = 'T':  A**T * X = B  (Transpose)
 *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
diff --git a/TESTING/LIN/cgtt02.f b/TESTING/LIN/cgtt02.f
index abfdfb75a8..0d067c3378 100644
--- a/TESTING/LIN/cgtt02.f
+++ b/TESTING/LIN/cgtt02.f
@@ -40,7 +40,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER
 *>          Specifies the form of the residual.
-*>          = 'N':  B - A * X     (No transpose)
+*>          = 'N':  B - A    * X  (No transpose)
 *>          = 'T':  B - A**T * X  (Transpose)
 *>          = 'C':  B - A**H * X  (Conjugate transpose)
 *> \endverbatim
@@ -182,7 +182,7 @@ SUBROUTINE CGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
          RETURN
       END IF
 *
-*     Compute B - op(A)*X.
+*     Compute B - op(A)*X and store in B.
 *
       CALL CLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
      $             LDB )
diff --git a/TESTING/LIN/clarhs.f b/TESTING/LIN/clarhs.f
index 0052d3667e..279c98f953 100644
--- a/TESTING/LIN/clarhs.f
+++ b/TESTING/LIN/clarhs.f
@@ -29,9 +29,8 @@
 *>
 *> CLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
-*> transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A, A**T, or A**H, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -85,9 +84,9 @@
 *>          TRANS is CHARACTER*1
 *>          Used only if A is nonsymmetric; specifies the operation
 *>          applied to the matrix A.
-*>          = 'N':  B := A    * X
-*>          = 'T':  B := A**T * X
-*>          = 'C':  B := A**H * X
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -313,7 +312,7 @@ SUBROUTINE CLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/LIN/cpot01.f b/TESTING/LIN/cpot01.f
index e9b19184f2..3c8e9a8859 100644
--- a/TESTING/LIN/cpot01.f
+++ b/TESTING/LIN/cpot01.f
@@ -67,10 +67,10 @@
 *> \param[in,out] AFAC
 *> \verbatim
 *>          AFAC is COMPLEX array, dimension (LDAFAC,N)
-*>          On entry, the factor L or U from the L*L' or U'*U
+*>          On entry, the factor L or U from the L * L**H or U**H * U
 *>          factorization of A.
-*>          Overwritten with the reconstructed matrix, and then with the
-*>          difference L*L' - A (or U'*U - A).
+*>          Overwritten with the reconstructed matrix, and then with
+*>          the difference L * L**H - A (or U**H * U - A).
 *> \endverbatim
 *>
 *> \param[in] LDAFAC
@@ -87,8 +87,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
-*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -169,7 +169,7 @@ SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
          END IF
    10 CONTINUE
 *
-*     Compute the product U'*U, overwriting U.
+*     Compute the product U**H * U, overwriting U.
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 20 K = N, 1, -1
@@ -186,7 +186,7 @@ SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
 *
    20    CONTINUE
 *
-*     Compute the product L*L', overwriting L.
+*     Compute the product L * L**H, overwriting L.
 *
       ELSE
          DO 30 K = N, 1, -1
@@ -206,7 +206,7 @@ SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    30    CONTINUE
       END IF
 *
-*     Compute the difference  L*L' - A (or U'*U - A).
+*     Compute the difference L * L**H - A (or U**H * U - A).
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 50 J = 1, N
@@ -224,7 +224,7 @@ SUBROUTINE CPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    70    CONTINUE
       END IF
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       RESID = CLANHE( '1', UPLO, N, AFAC, LDAFAC, RWORK )
 *
diff --git a/TESTING/LIN/cqrt17.f b/TESTING/LIN/cqrt17.f
index c4e5dd6f09..85443c8387 100644
--- a/TESTING/LIN/cqrt17.f
+++ b/TESTING/LIN/cqrt17.f
@@ -28,12 +28,13 @@
 *>
 *> CQRT17 computes the ratio
 *>
-*>    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
+*>    norm(R**H * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),
 *>
-*> where R = op(A)*X - B, op(A) is A or A', and
+*> where R = B - op(A)*X, op(A) is A or A**H, depending on TRANS, EPS
+*> is the machine epsilon, and
 *>
-*>    alpha = ||B|| if IRESID = 1 (zero-residual problem)
-*>    alpha = ||R|| if IRESID = 2 (otherwise).
+*>    alpha = norm(B) if IRESID = 1 (zero-residual problem)
+*>    alpha = norm(R) if IRESID = 2 (otherwise).
 *> \endverbatim
 *
 *  Arguments:
@@ -44,7 +45,7 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies whether or not the transpose of A is used.
 *>          = 'N':  No transpose, op(A) = A.
-*>          = 'C':  Conjugate transpose, op(A) = A'.
+*>          = 'C':  Conjugate transpose, op(A) = A**H.
 *> \endverbatim
 *>
 *> \param[in] IRESID
@@ -224,7 +225,7 @@ REAL             FUNCTION CQRT17( TRANS, IRESID, M, N, NRHS, A,
      $                INFO )
       END IF
 *
-*     compute R'*op(A)
+*     compute R**H * op(A)
 *
       CALL CGEMM( 'Conjugate transpose', TRANS, NRHS, NCOLS, NROWS,
      $            CMPLX( ONE ), C, LDB, A, LDA, CMPLX( ZERO ), WORK,
diff --git a/TESTING/LIN/ctbt02.f b/TESTING/LIN/ctbt02.f
index 8f95c95af3..359eb467f0 100644
--- a/TESTING/LIN/ctbt02.f
+++ b/TESTING/LIN/ctbt02.f
@@ -53,9 +53,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to A.
-*>          = 'N':  A *x = b     (No transpose)
-*>          = 'T':  A**T *x = b  (Transpose)
-*>          = 'C':  A**H *x = b  (Conjugate transpose)
+*>          = 'N':  A    * X = B  (No transpose)
+*>          = 'T':  A**T * X = B  (Transpose)
+*>          = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] DIAG
@@ -142,7 +142,7 @@
 *> \verbatim
 *>          RESID is REAL
 *>          The maximum over the number of right hand sides of
-*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *> \endverbatim
 *
 *  Authors:
@@ -204,7 +204,7 @@ SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
          RETURN
       END IF
 *
-*     Compute the 1-norm of A or A'.
+*     Compute the 1-norm of op(A).
 *
       IF( LSAME( TRANS, 'N' ) ) THEN
          ANORM = CLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
@@ -221,7 +221,7 @@ SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
       END IF
 *
 *     Compute the maximum over the number of right hand sides of
-*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *
       RESID = ZERO
       DO 10 J = 1, NRHS
diff --git a/TESTING/LIN/dchkge.f b/TESTING/LIN/dchkge.f
index 705a9dbbc2..467667a42b 100644
--- a/TESTING/LIN/dchkge.f
+++ b/TESTING/LIN/dchkge.f
@@ -77,7 +77,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchklqt.f b/TESTING/LIN/dchklqt.f
index ba67011852..aa77d6a62e 100644
--- a/TESTING/LIN/dchklqt.f
+++ b/TESTING/LIN/dchklqt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchklqtp.f b/TESTING/LIN/dchklqtp.f
index 8090213305..d9251b1f09 100644
--- a/TESTING/LIN/dchklqtp.f
+++ b/TESTING/LIN/dchklqtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkorhr_col.f b/TESTING/LIN/dchkorhr_col.f
index 0e2d44d8d2..a849f39106 100644
--- a/TESTING/LIN/dchkorhr_col.f
+++ b/TESTING/LIN/dchkorhr_col.f
@@ -82,7 +82,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkpb.f b/TESTING/LIN/dchkpb.f
index 74b8979d65..c5d51230ed 100644
--- a/TESTING/LIN/dchkpb.f
+++ b/TESTING/LIN/dchkpb.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkpo.f b/TESTING/LIN/dchkpo.f
index e5abd9c7a1..e9d5af1863 100644
--- a/TESTING/LIN/dchkpo.f
+++ b/TESTING/LIN/dchkpo.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkps.f b/TESTING/LIN/dchkps.f
index 47d43d0a62..1e4a9e58de 100644
--- a/TESTING/LIN/dchkps.f
+++ b/TESTING/LIN/dchkps.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the block size NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkqrt.f b/TESTING/LIN/dchkqrt.f
index 690b041df7..566f273d4e 100644
--- a/TESTING/LIN/dchkqrt.f
+++ b/TESTING/LIN/dchkqrt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchkqrtp.f b/TESTING/LIN/dchkqrtp.f
index 1e53bcded7..924ba7ea37 100644
--- a/TESTING/LIN/dchkqrtp.f
+++ b/TESTING/LIN/dchkqrtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchksy.f b/TESTING/LIN/dchksy.f
index 84589d8e02..8d127cd3b6 100644
--- a/TESTING/LIN/dchksy.f
+++ b/TESTING/LIN/dchksy.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchksy_aa.f b/TESTING/LIN/dchksy_aa.f
index 81139440fa..4c79ebbbf1 100644
--- a/TESTING/LIN/dchksy_aa.f
+++ b/TESTING/LIN/dchksy_aa.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchksy_aa_2stage.f b/TESTING/LIN/dchksy_aa_2stage.f
index 405f8f12d7..bc4e77a5aa 100644
--- a/TESTING/LIN/dchksy_aa_2stage.f
+++ b/TESTING/LIN/dchksy_aa_2stage.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchksy_rk.f b/TESTING/LIN/dchksy_rk.f
index 3731a3c666..701cb9ce6a 100644
--- a/TESTING/LIN/dchksy_rk.f
+++ b/TESTING/LIN/dchksy_rk.f
@@ -63,7 +63,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchksy_rook.f b/TESTING/LIN/dchksy_rook.f
index 1af46409ba..03b16b78ac 100644
--- a/TESTING/LIN/dchksy_rook.f
+++ b/TESTING/LIN/dchksy_rook.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dchktsqr.f b/TESTING/LIN/dchktsqr.f
index c7f06c11c7..27076b5c26 100644
--- a/TESTING/LIN/dchktsqr.f
+++ b/TESTING/LIN/dchktsqr.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/dgbt01.f b/TESTING/LIN/dgbt01.f
index 28f7200ddb..6a095876ed 100644
--- a/TESTING/LIN/dgbt01.f
+++ b/TESTING/LIN/dgbt01.f
@@ -26,7 +26,7 @@
 *>
 *> \verbatim
 *>
-*> DGBT01 reconstructs a band matrix  A  from its L*U factorization and
+*> DGBT01 reconstructs a band matrix A from its L*U factorization and
 *> computes the residual:
 *>    norm(L*U - A) / ( N * norm(A) * EPS ),
 *> where EPS is the machine epsilon.
@@ -225,7 +225,7 @@ SUBROUTINE DGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
          END IF
    40 CONTINUE
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       IF( ANORM.LE.ZERO ) THEN
          IF( RESID.NE.ZERO )
diff --git a/TESTING/LIN/dgbt02.f b/TESTING/LIN/dgbt02.f
index ef7e00c3d6..1184587a9c 100644
--- a/TESTING/LIN/dgbt02.f
+++ b/TESTING/LIN/dgbt02.f
@@ -31,7 +31,7 @@
 *> equations op(A)*X = B:
 *>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 *> where op(A) = A or A**T, depending on TRANS, and EPS is the
-*> machine precision.
+*> machine epsilon.
 *> \endverbatim
 *
 *  Arguments:
diff --git a/TESTING/LIN/dgbt05.f b/TESTING/LIN/dgbt05.f
index ba85eaf7d9..793e73951d 100644
--- a/TESTING/LIN/dgbt05.f
+++ b/TESTING/LIN/dgbt05.f
@@ -50,7 +50,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the form of the system of equations.
-*>          = 'N':  A * X = B     (No transpose)
+*>          = 'N':  A    * X = B  (No transpose)
 *>          = 'T':  A**T * X = B  (Transpose)
 *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
diff --git a/TESTING/LIN/dgtt02.f b/TESTING/LIN/dgtt02.f
index 1cc17215a3..e91f002249 100644
--- a/TESTING/LIN/dgtt02.f
+++ b/TESTING/LIN/dgtt02.f
@@ -40,9 +40,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER
 *>          Specifies the form of the residual.
-*>          = 'N':  B - A * X  (No transpose)
-*>          = 'T':  B - A'* X  (Transpose)
-*>          = 'C':  B - A'* X  (Conjugate transpose = Transpose)
+*>          = 'N':  B - A    * X  (No transpose)
+*>          = 'T':  B - A**T * X  (Transpose)
+*>          = 'C':  B - A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] N
@@ -182,7 +182,7 @@ SUBROUTINE DGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
          RETURN
       END IF
 *
-*     Compute B - op(A)*X.
+*     Compute B - op(A)*X and store in B.
 *
       CALL DLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
      $             LDB )
diff --git a/TESTING/LIN/dlarhs.f b/TESTING/LIN/dlarhs.f
index b9ce743386..48a1d54a68 100644
--- a/TESTING/LIN/dlarhs.f
+++ b/TESTING/LIN/dlarhs.f
@@ -29,8 +29,8 @@
 *>
 *> DLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -79,10 +79,11 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          Specifies the operation applied to the matrix A.
-*>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          Used only if A is nonsymmetric; specifies the operation
+*>          applied to the matrix A.
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -305,7 +306,7 @@ SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/LIN/dpot01.f b/TESTING/LIN/dpot01.f
index f48a1a4fc5..b48d066101 100644
--- a/TESTING/LIN/dpot01.f
+++ b/TESTING/LIN/dpot01.f
@@ -65,10 +65,10 @@
 *> \param[in,out] AFAC
 *> \verbatim
 *>          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
-*>          On entry, the factor L or U from the L*L' or U'*U
+*>          On entry, the factor L or U from the L * L**T or U**T * U
 *>          factorization of A.
-*>          Overwritten with the reconstructed matrix, and then with the
-*>          difference L*L' - A (or U'*U - A).
+*>          Overwritten with the reconstructed matrix, and then with
+*>          the difference L * L**T - A (or U**T * U - A).
 *> \endverbatim
 *>
 *> \param[in] LDAFAC
@@ -85,8 +85,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
-*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'L', norm(L * L**T - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'U', norm(U**T * U - A) / ( N * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -154,7 +154,7 @@ SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
          RETURN
       END IF
 *
-*     Compute the product U'*U, overwriting U.
+*     Compute the product U**T * U, overwriting U.
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 10 K = N, 1, -1
@@ -171,7 +171,7 @@ SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
 *
    10    CONTINUE
 *
-*     Compute the product L*L', overwriting L.
+*     Compute the product L * L**T, overwriting L.
 *
       ELSE
          DO 20 K = N, 1, -1
@@ -191,7 +191,7 @@ SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    20    CONTINUE
       END IF
 *
-*     Compute the difference  L*L' - A (or U'*U - A).
+*     Compute the difference L * L**T - A (or U**T * U - A).
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 40 J = 1, N
@@ -207,7 +207,7 @@ SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    60    CONTINUE
       END IF
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       RESID = DLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK )
 *
diff --git a/TESTING/LIN/dqrt17.f b/TESTING/LIN/dqrt17.f
index 592904a497..15479f8e52 100644
--- a/TESTING/LIN/dqrt17.f
+++ b/TESTING/LIN/dqrt17.f
@@ -28,12 +28,13 @@
 *>
 *> DQRT17 computes the ratio
 *>
-*>    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
+*>    norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),
 *>
-*> where R = op(A)*X - B, op(A) is A or A', and
+*> where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS
+*> is the machine epsilon, and
 *>
-*>    alpha = ||B|| if IRESID = 1 (zero-residual problem)
-*>    alpha = ||R|| if IRESID = 2 (otherwise).
+*>    alpha = norm(B) if IRESID = 1 (zero-residual problem)
+*>    alpha = norm(R) if IRESID = 2 (otherwise).
 *> \endverbatim
 *
 *  Arguments:
@@ -44,7 +45,7 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies whether or not the transpose of A is used.
 *>          = 'N':  No transpose, op(A) = A.
-*>          = 'T':  Transpose, op(A) = A'.
+*>          = 'T':  Transpose, op(A) = A**T.
 *> \endverbatim
 *>
 *> \param[in] IRESID
@@ -225,7 +226,7 @@ DOUBLE PRECISION FUNCTION DQRT17( TRANS, IRESID, M, N, NRHS, A,
      $                INFO )
       END IF
 *
-*     compute R'*op(A)
+*     compute R**T * op(A)
 *
       CALL DGEMM( 'Transpose', TRANS, NRHS, NCOLS, NROWS, ONE, C, LDB,
      $            A, LDA, ZERO, WORK, NRHS )
diff --git a/TESTING/LIN/dtbt02.f b/TESTING/LIN/dtbt02.f
index 2870b32677..12f4ec2b5d 100644
--- a/TESTING/LIN/dtbt02.f
+++ b/TESTING/LIN/dtbt02.f
@@ -51,9 +51,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to A.
-*>          = 'N':  A *x = b  (No transpose)
-*>          = 'T':  A'*x = b  (Transpose)
-*>          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
+*>          = 'N':  A    * X = B  (No transpose)
+*>          = 'T':  A**T * X = B  (Transpose)
+*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] DIAG
@@ -135,7 +135,7 @@
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
 *>          The maximum over the number of right hand sides of
-*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *> \endverbatim
 *
 *  Authors:
@@ -196,7 +196,7 @@ SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
          RETURN
       END IF
 *
-*     Compute the 1-norm of A or A'.
+*     Compute the 1-norm of op(A).
 *
       IF( LSAME( TRANS, 'N' ) ) THEN
          ANORM = DLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, WORK )
@@ -213,7 +213,7 @@ SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
       END IF
 *
 *     Compute the maximum over the number of right hand sides of
-*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *
       RESID = ZERO
       DO 10 J = 1, NRHS
diff --git a/TESTING/LIN/schkge.f b/TESTING/LIN/schkge.f
index 6a2c0b0cfd..0921f79257 100644
--- a/TESTING/LIN/schkge.f
+++ b/TESTING/LIN/schkge.f
@@ -77,7 +77,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schklqt.f b/TESTING/LIN/schklqt.f
index 966142f8f2..2230583bae 100644
--- a/TESTING/LIN/schklqt.f
+++ b/TESTING/LIN/schklqt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schklqtp.f b/TESTING/LIN/schklqtp.f
index aeb3b43710..20c0dd0199 100644
--- a/TESTING/LIN/schklqtp.f
+++ b/TESTING/LIN/schklqtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkorhr_col.f b/TESTING/LIN/schkorhr_col.f
index f61b749028..9c91b85353 100644
--- a/TESTING/LIN/schkorhr_col.f
+++ b/TESTING/LIN/schkorhr_col.f
@@ -82,7 +82,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkpb.f b/TESTING/LIN/schkpb.f
index 6a9662bdeb..fdad0d6dfd 100644
--- a/TESTING/LIN/schkpb.f
+++ b/TESTING/LIN/schkpb.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkpo.f b/TESTING/LIN/schkpo.f
index 266abcb43f..ccfb9b7b27 100644
--- a/TESTING/LIN/schkpo.f
+++ b/TESTING/LIN/schkpo.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkps.f b/TESTING/LIN/schkps.f
index 9385a5809c..7bd70c4525 100644
--- a/TESTING/LIN/schkps.f
+++ b/TESTING/LIN/schkps.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the block size NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkqrt.f b/TESTING/LIN/schkqrt.f
index 23515d95d4..ed25a230d4 100644
--- a/TESTING/LIN/schkqrt.f
+++ b/TESTING/LIN/schkqrt.f
@@ -74,7 +74,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schkqrtp.f b/TESTING/LIN/schkqrtp.f
index 5be01b6cd7..eee963c472 100644
--- a/TESTING/LIN/schkqrtp.f
+++ b/TESTING/LIN/schkqrtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schksy.f b/TESTING/LIN/schksy.f
index 39353671d3..dc94b34924 100644
--- a/TESTING/LIN/schksy.f
+++ b/TESTING/LIN/schksy.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schksy_aa.f b/TESTING/LIN/schksy_aa.f
index 573b905aa8..75b895bd43 100644
--- a/TESTING/LIN/schksy_aa.f
+++ b/TESTING/LIN/schksy_aa.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schksy_aa_2stage.f b/TESTING/LIN/schksy_aa_2stage.f
index 8a5ed94dec..d3c27ae561 100644
--- a/TESTING/LIN/schksy_aa_2stage.f
+++ b/TESTING/LIN/schksy_aa_2stage.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schksy_rk.f b/TESTING/LIN/schksy_rk.f
index 0158ead9f5..932e6e1860 100644
--- a/TESTING/LIN/schksy_rk.f
+++ b/TESTING/LIN/schksy_rk.f
@@ -63,7 +63,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schksy_rook.f b/TESTING/LIN/schksy_rook.f
index c0ad39ce96..eb91eba4f0 100644
--- a/TESTING/LIN/schksy_rook.f
+++ b/TESTING/LIN/schksy_rook.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/schktsqr.f b/TESTING/LIN/schktsqr.f
index a3994cbed3..5d7aa2d374 100644
--- a/TESTING/LIN/schktsqr.f
+++ b/TESTING/LIN/schktsqr.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/sgbt01.f b/TESTING/LIN/sgbt01.f
index 0f6129240a..c5ae6b11a5 100644
--- a/TESTING/LIN/sgbt01.f
+++ b/TESTING/LIN/sgbt01.f
@@ -26,7 +26,7 @@
 *>
 *> \verbatim
 *>
-*> SGBT01 reconstructs a band matrix  A  from its L*U factorization and
+*> SGBT01 reconstructs a band matrix A from its L*U factorization and
 *> computes the residual:
 *>    norm(L*U - A) / ( N * norm(A) * EPS ),
 *> where EPS is the machine epsilon.
@@ -225,7 +225,7 @@ SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
          END IF
    40 CONTINUE
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       IF( ANORM.LE.ZERO ) THEN
          IF( RESID.NE.ZERO )
diff --git a/TESTING/LIN/sgbt02.f b/TESTING/LIN/sgbt02.f
index 2c0734d150..82a5555490 100644
--- a/TESTING/LIN/sgbt02.f
+++ b/TESTING/LIN/sgbt02.f
@@ -31,7 +31,7 @@
 *> equations op(A)*X = B:
 *>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 *> where op(A) = A or A**T, depending on TRANS, and EPS is the
-*> machine precision.
+*> machine epsilon.
 *> \endverbatim
 *
 *  Arguments:
diff --git a/TESTING/LIN/sgbt05.f b/TESTING/LIN/sgbt05.f
index cfd6dd743e..bba80b56da 100644
--- a/TESTING/LIN/sgbt05.f
+++ b/TESTING/LIN/sgbt05.f
@@ -50,7 +50,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the form of the system of equations.
-*>          = 'N':  A * X = B     (No transpose)
+*>          = 'N':  A    * X = B  (No transpose)
 *>          = 'T':  A**T * X = B  (Transpose)
 *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
diff --git a/TESTING/LIN/sgtt02.f b/TESTING/LIN/sgtt02.f
index 52e2d443e7..0b03e7f592 100644
--- a/TESTING/LIN/sgtt02.f
+++ b/TESTING/LIN/sgtt02.f
@@ -40,9 +40,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER
 *>          Specifies the form of the residual.
-*>          = 'N':  B - A * X  (No transpose)
-*>          = 'T':  B - A'* X  (Transpose)
-*>          = 'C':  B - A'* X  (Conjugate transpose = Transpose)
+*>          = 'N':  B - A    * X  (No transpose)
+*>          = 'T':  B - A**T * X  (Transpose)
+*>          = 'C':  B - A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] N
@@ -182,7 +182,7 @@ SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
          RETURN
       END IF
 *
-*     Compute B - op(A)*X.
+*     Compute B - op(A)*X and store in B.
 *
       CALL SLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
      $             LDB )
diff --git a/TESTING/LIN/slarhs.f b/TESTING/LIN/slarhs.f
index b126ca72a4..6a8a592c8c 100644
--- a/TESTING/LIN/slarhs.f
+++ b/TESTING/LIN/slarhs.f
@@ -29,8 +29,8 @@
 *>
 *> SLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -79,10 +79,11 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          Specifies the operation applied to the matrix A.
-*>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          Used only if A is nonsymmetric; specifies the operation
+*>          applied to the matrix A.
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -305,7 +306,7 @@ SUBROUTINE SLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/LIN/spot01.f b/TESTING/LIN/spot01.f
index a0176c822e..5f14b3f0ff 100644
--- a/TESTING/LIN/spot01.f
+++ b/TESTING/LIN/spot01.f
@@ -65,10 +65,10 @@
 *> \param[in,out] AFAC
 *> \verbatim
 *>          AFAC is REAL array, dimension (LDAFAC,N)
-*>          On entry, the factor L or U from the L*L' or U'*U
+*>          On entry, the factor L or U from the L * L**T or U**T * U
 *>          factorization of A.
-*>          Overwritten with the reconstructed matrix, and then with the
-*>          difference L*L' - A (or U'*U - A).
+*>          Overwritten with the reconstructed matrix, and then with
+*>          the difference L * L**T - A (or U**T * U - A).
 *> \endverbatim
 *>
 *> \param[in] LDAFAC
@@ -85,8 +85,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
-*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'L', norm(L * L**T - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'U', norm(U**T * U - A) / ( N * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -154,7 +154,7 @@ SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
          RETURN
       END IF
 *
-*     Compute the product U'*U, overwriting U.
+*     Compute the product U**T * U, overwriting U.
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 10 K = N, 1, -1
@@ -171,7 +171,7 @@ SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
 *
    10    CONTINUE
 *
-*     Compute the product L*L', overwriting L.
+*     Compute the product L * L**T, overwriting L.
 *
       ELSE
          DO 20 K = N, 1, -1
@@ -191,7 +191,7 @@ SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    20    CONTINUE
       END IF
 *
-*     Compute the difference  L*L' - A (or U'*U - A).
+*     Compute the difference L * L**T - A (or U**T * U - A).
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 40 J = 1, N
@@ -207,7 +207,7 @@ SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    60    CONTINUE
       END IF
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       RESID = SLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK )
 *
diff --git a/TESTING/LIN/sqrt17.f b/TESTING/LIN/sqrt17.f
index 1a80b8c784..83c3ca98fd 100644
--- a/TESTING/LIN/sqrt17.f
+++ b/TESTING/LIN/sqrt17.f
@@ -28,12 +28,13 @@
 *>
 *> SQRT17 computes the ratio
 *>
-*>    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
+*>    norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),
 *>
-*> where R = op(A)*X - B, op(A) is A or A', and
+*> where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS
+*> is the machine epsilon, and
 *>
-*>    alpha = ||B|| if IRESID = 1 (zero-residual problem)
-*>    alpha = ||R|| if IRESID = 2 (otherwise).
+*>    alpha = norm(B) if IRESID = 1 (zero-residual problem)
+*>    alpha = norm(R) if IRESID = 2 (otherwise).
 *> \endverbatim
 *
 *  Arguments:
@@ -44,7 +45,7 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies whether or not the transpose of A is used.
 *>          = 'N':  No transpose, op(A) = A.
-*>          = 'T':  Transpose, op(A) = A'.
+*>          = 'T':  Transpose, op(A) = A**T.
 *> \endverbatim
 *>
 *> \param[in] IRESID
@@ -225,7 +226,7 @@ REAL             FUNCTION SQRT17( TRANS, IRESID, M, N, NRHS, A,
      $                INFO )
       END IF
 *
-*     compute R'*op(A)
+*     compute R**T * op(A)
 *
       CALL SGEMM( 'Transpose', TRANS, NRHS, NCOLS, NROWS, ONE, C, LDB,
      $            A, LDA, ZERO, WORK, NRHS )
diff --git a/TESTING/LIN/stbt02.f b/TESTING/LIN/stbt02.f
index 96ca3b6baa..5c3932c711 100644
--- a/TESTING/LIN/stbt02.f
+++ b/TESTING/LIN/stbt02.f
@@ -28,10 +28,9 @@
 *> \verbatim
 *>
 *> STBT02 computes the residual for the computed solution to a
-*> triangular system of linear equations  A*x = b  or  A' *x = b when
-*> A is a triangular band matrix.  Here A' is the transpose of A and
-*> x and b are N by NRHS matrices.  The test ratio is the maximum over
-*> the number of right hand sides of
+*> triangular system of linear equations op(A)*X = B when A is a
+*> triangular band matrix.  The test ratio is the maximum over the
+*> number of right hand sides of
 *>    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 *> where op(A) denotes A or A' and EPS is the machine epsilon.
 *> \endverbatim
@@ -51,9 +50,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to A.
-*>          = 'N':  A *x = b  (No transpose)
-*>          = 'T':  A'*x = b  (Transpose)
-*>          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
+*>          = 'N':  A    * X = B  (No transpose)
+*>          = 'T':  A**T * X = B  (Transpose)
+*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] DIAG
@@ -135,7 +134,7 @@
 *> \verbatim
 *>          RESID is REAL
 *>          The maximum over the number of right hand sides of
-*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *> \endverbatim
 *
 *  Authors:
@@ -196,7 +195,7 @@ SUBROUTINE STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
          RETURN
       END IF
 *
-*     Compute the 1-norm of A or A'.
+*     Compute the 1-norm of op(A).
 *
       IF( LSAME( TRANS, 'N' ) ) THEN
          ANORM = SLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, WORK )
@@ -213,7 +212,7 @@ SUBROUTINE STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
       END IF
 *
 *     Compute the maximum over the number of right hand sides of
-*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *
       RESID = ZERO
       DO 10 J = 1, NRHS
diff --git a/TESTING/LIN/zchkgb.f b/TESTING/LIN/zchkgb.f
index d4d261d93a..3b0cd707ab 100644
--- a/TESTING/LIN/zchkgb.f
+++ b/TESTING/LIN/zchkgb.f
@@ -78,7 +78,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkge.f b/TESTING/LIN/zchkge.f
index df46a3fc8a..d87759df5c 100644
--- a/TESTING/LIN/zchkge.f
+++ b/TESTING/LIN/zchkge.f
@@ -78,7 +78,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkhe.f b/TESTING/LIN/zchkhe.f
index f0e746890a..e443eab04f 100644
--- a/TESTING/LIN/zchkhe.f
+++ b/TESTING/LIN/zchkhe.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkhe_aa.f b/TESTING/LIN/zchkhe_aa.f
index acb0dd31cf..1c4ee88e0e 100644
--- a/TESTING/LIN/zchkhe_aa.f
+++ b/TESTING/LIN/zchkhe_aa.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkhe_aa_2stage.f b/TESTING/LIN/zchkhe_aa_2stage.f
index f4d9585f33..726e1fea6d 100644
--- a/TESTING/LIN/zchkhe_aa_2stage.f
+++ b/TESTING/LIN/zchkhe_aa_2stage.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkhe_rk.f b/TESTING/LIN/zchkhe_rk.f
index e670bf3279..63697d33a1 100644
--- a/TESTING/LIN/zchkhe_rk.f
+++ b/TESTING/LIN/zchkhe_rk.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkhe_rook.f b/TESTING/LIN/zchkhe_rook.f
index c18528b3c6..84f5a84220 100644
--- a/TESTING/LIN/zchkhe_rook.f
+++ b/TESTING/LIN/zchkhe_rook.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchklqt.f b/TESTING/LIN/zchklqt.f
index 1e941f0bcb..680c1135e2 100644
--- a/TESTING/LIN/zchklqt.f
+++ b/TESTING/LIN/zchklqt.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchklqtp.f b/TESTING/LIN/zchklqtp.f
index a3ad56ed63..75e3ddfb1d 100644
--- a/TESTING/LIN/zchklqtp.f
+++ b/TESTING/LIN/zchklqtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkpb.f b/TESTING/LIN/zchkpb.f
index a935d10c89..1ce8c3b88f 100644
--- a/TESTING/LIN/zchkpb.f
+++ b/TESTING/LIN/zchkpb.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkpo.f b/TESTING/LIN/zchkpo.f
index 7ceb65f7c5..93ea721633 100644
--- a/TESTING/LIN/zchkpo.f
+++ b/TESTING/LIN/zchkpo.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkps.f b/TESTING/LIN/zchkps.f
index 8cf05ccd26..79fc951e22 100644
--- a/TESTING/LIN/zchkps.f
+++ b/TESTING/LIN/zchkps.f
@@ -64,7 +64,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the block size NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkqrt.f b/TESTING/LIN/zchkqrt.f
index cf096ef4eb..cb07af72ce 100644
--- a/TESTING/LIN/zchkqrt.f
+++ b/TESTING/LIN/zchkqrt.f
@@ -75,7 +75,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkqrtp.f b/TESTING/LIN/zchkqrtp.f
index 54cb9ab725..9337a68375 100644
--- a/TESTING/LIN/zchkqrtp.f
+++ b/TESTING/LIN/zchkqrtp.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchksy.f b/TESTING/LIN/zchksy.f
index 2232497b6f..7877eb7e2d 100644
--- a/TESTING/LIN/zchksy.f
+++ b/TESTING/LIN/zchksy.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchksy_aa.f b/TESTING/LIN/zchksy_aa.f
index 3f0c52173a..9f53593d57 100644
--- a/TESTING/LIN/zchksy_aa.f
+++ b/TESTING/LIN/zchksy_aa.f
@@ -65,7 +65,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchksy_aa_2stage.f b/TESTING/LIN/zchksy_aa_2stage.f
index 8671d09796..4c8ff94f78 100644
--- a/TESTING/LIN/zchksy_aa_2stage.f
+++ b/TESTING/LIN/zchksy_aa_2stage.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchksy_rk.f b/TESTING/LIN/zchksy_rk.f
index 276fa569e3..3a206b30d8 100644
--- a/TESTING/LIN/zchksy_rk.f
+++ b/TESTING/LIN/zchksy_rk.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchksy_rook.f b/TESTING/LIN/zchksy_rook.f
index 4daac3f951..dcb5b6edd1 100644
--- a/TESTING/LIN/zchksy_rook.f
+++ b/TESTING/LIN/zchksy_rook.f
@@ -66,7 +66,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchktsqr.f b/TESTING/LIN/zchktsqr.f
index 151a925aef..ca7828f1ad 100644
--- a/TESTING/LIN/zchktsqr.f
+++ b/TESTING/LIN/zchktsqr.f
@@ -76,7 +76,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zchkunhr_col.f b/TESTING/LIN/zchkunhr_col.f
index 395ea178af..a6ec2f0f81 100644
--- a/TESTING/LIN/zchkunhr_col.f
+++ b/TESTING/LIN/zchkunhr_col.f
@@ -82,7 +82,7 @@
 *>
 *> \param[in] NBVAL
 *> \verbatim
-*>          NBVAL is INTEGER array, dimension (NBVAL)
+*>          NBVAL is INTEGER array, dimension (NNB)
 *>          The values of the blocksize NB.
 *> \endverbatim
 *>
diff --git a/TESTING/LIN/zgbt01.f b/TESTING/LIN/zgbt01.f
index 9219193713..e041ab9fa0 100644
--- a/TESTING/LIN/zgbt01.f
+++ b/TESTING/LIN/zgbt01.f
@@ -26,7 +26,7 @@
 *>
 *> \verbatim
 *>
-*> ZGBT01 reconstructs a band matrix  A  from its L*U factorization and
+*> ZGBT01 reconstructs a band matrix A from its L*U factorization and
 *> computes the residual:
 *>    norm(L*U - A) / ( N * norm(A) * EPS ),
 *> where EPS is the machine epsilon.
@@ -226,7 +226,7 @@ SUBROUTINE ZGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
          END IF
    40 CONTINUE
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       IF( ANORM.LE.ZERO ) THEN
          IF( RESID.NE.ZERO )
diff --git a/TESTING/LIN/zgbt02.f b/TESTING/LIN/zgbt02.f
index 3547ea0b5e..0d13b571ad 100644
--- a/TESTING/LIN/zgbt02.f
+++ b/TESTING/LIN/zgbt02.f
@@ -31,7 +31,7 @@
 *> equations op(A)*X = B:
 *>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 *> where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
-*> machine precision.
+*> machine epsilon.
 *> \endverbatim
 *
 *  Arguments:
diff --git a/TESTING/LIN/zgbt05.f b/TESTING/LIN/zgbt05.f
index f74287f421..0dc6852118 100644
--- a/TESTING/LIN/zgbt05.f
+++ b/TESTING/LIN/zgbt05.f
@@ -30,7 +30,7 @@
 *> ZGBT05 tests the error bounds from iterative refinement for the
 *> computed solution to a system of equations op(A)*X = B, where A is a
 *> general band matrix of order n with kl subdiagonals and ku
-*> superdiagonals and op(A) = A or A**T, depending on TRANS.
+*> superdiagonals and op(A) = A, A**T, or A**H, depending on TRANS.
 *>
 *> RESLTS(1) = test of the error bound
 *>           = norm(X - XACT) / ( norm(X) * FERR )
@@ -50,7 +50,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the form of the system of equations.
-*>          = 'N':  A * X = B     (No transpose)
+*>          = 'N':  A    * X = B  (No transpose)
 *>          = 'T':  A**T * X = B  (Transpose)
 *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
 *> \endverbatim
diff --git a/TESTING/LIN/zgtt02.f b/TESTING/LIN/zgtt02.f
index ded2256064..72cc9ea712 100644
--- a/TESTING/LIN/zgtt02.f
+++ b/TESTING/LIN/zgtt02.f
@@ -40,7 +40,7 @@
 *> \verbatim
 *>          TRANS is CHARACTER
 *>          Specifies the form of the residual.
-*>          = 'N':  B - A * X     (No transpose)
+*>          = 'N':  B - A    * X  (No transpose)
 *>          = 'T':  B - A**T * X  (Transpose)
 *>          = 'C':  B - A**H * X  (Conjugate transpose)
 *> \endverbatim
@@ -182,7 +182,7 @@ SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
          RETURN
       END IF
 *
-*     Compute B - op(A)*X.
+*     Compute B - op(A)*X and store in B.
 *
       CALL ZLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
      $             LDB )
diff --git a/TESTING/LIN/zlarhs.f b/TESTING/LIN/zlarhs.f
index 92d746fc45..210a4a3c14 100644
--- a/TESTING/LIN/zlarhs.f
+++ b/TESTING/LIN/zlarhs.f
@@ -29,9 +29,8 @@
 *>
 *> ZLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
-*>    op( A ) * X = B,
-*> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
-*> transpose of A).
+*>    op(A) * X = B,
+*> where op(A) = A, A**T, or A**H, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -85,9 +84,9 @@
 *>          TRANS is CHARACTER*1
 *>          Used only if A is nonsymmetric; specifies the operation
 *>          applied to the matrix A.
-*>          = 'N':  B := A    * X
-*>          = 'T':  B := A**T * X
-*>          = 'C':  B := A**H * X
+*>          = 'N':  B := A    * X  (No transpose)
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] M
@@ -313,7 +312,7 @@ SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
    10    CONTINUE
       END IF
 *
-*     Multiply X by op( A ) using an appropriate
+*     Multiply X by op(A) using an appropriate
 *     matrix multiply routine.
 *
       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
diff --git a/TESTING/LIN/zpot01.f b/TESTING/LIN/zpot01.f
index c08a27bf71..b083856211 100644
--- a/TESTING/LIN/zpot01.f
+++ b/TESTING/LIN/zpot01.f
@@ -67,10 +67,10 @@
 *> \param[in,out] AFAC
 *> \verbatim
 *>          AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
-*>          On entry, the factor L or U from the L*L' or U'*U
+*>          On entry, the factor L or U from the L * L**H or U**H * U
 *>          factorization of A.
-*>          Overwritten with the reconstructed matrix, and then with the
-*>          difference L*L' - A (or U'*U - A).
+*>          Overwritten with the reconstructed matrix, and then with
+*>          the difference L * L**H - A (or U**H * U - A).
 *> \endverbatim
 *>
 *> \param[in] LDAFAC
@@ -87,8 +87,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
-*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'L', norm(L * L**H - A) / ( N * norm(A) * EPS )
+*>          If UPLO = 'U', norm(U**H * U - A) / ( N * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -169,7 +169,7 @@ SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
          END IF
    10 CONTINUE
 *
-*     Compute the product U'*U, overwriting U.
+*     Compute the product U**H * U, overwriting U.
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 20 K = N, 1, -1
@@ -186,7 +186,7 @@ SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
 *
    20    CONTINUE
 *
-*     Compute the product L*L', overwriting L.
+*     Compute the product L * L**H, overwriting L.
 *
       ELSE
          DO 30 K = N, 1, -1
@@ -206,7 +206,7 @@ SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    30    CONTINUE
       END IF
 *
-*     Compute the difference  L*L' - A (or U'*U - A).
+*     Compute the difference L * L**H - A (or U**H * U - A).
 *
       IF( LSAME( UPLO, 'U' ) ) THEN
          DO 50 J = 1, N
@@ -224,7 +224,7 @@ SUBROUTINE ZPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
    70    CONTINUE
       END IF
 *
-*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
+*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
 *
       RESID = ZLANHE( '1', UPLO, N, AFAC, LDAFAC, RWORK )
 *
diff --git a/TESTING/LIN/zqrt17.f b/TESTING/LIN/zqrt17.f
index 77dd77b417..060d46cb9a 100644
--- a/TESTING/LIN/zqrt17.f
+++ b/TESTING/LIN/zqrt17.f
@@ -28,12 +28,13 @@
 *>
 *> ZQRT17 computes the ratio
 *>
-*>    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
+*>    norm(R**H * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),
 *>
-*> where R = op(A)*X - B, op(A) is A or A', and
+*> where R = B - op(A)*X, op(A) is A or A**H, depending on TRANS, EPS
+*> is the machine epsilon, and
 *>
-*>    alpha = ||B|| if IRESID = 1 (zero-residual problem)
-*>    alpha = ||R|| if IRESID = 2 (otherwise).
+*>    alpha = norm(B) if IRESID = 1 (zero-residual problem)
+*>    alpha = norm(R) if IRESID = 2 (otherwise).
 *> \endverbatim
 *
 *  Arguments:
@@ -44,7 +45,7 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies whether or not the transpose of A is used.
 *>          = 'N':  No transpose, op(A) = A.
-*>          = 'C':  Conjugate transpose, op(A) = A'.
+*>          = 'C':  Conjugate transpose, op(A) = A**H.
 *> \endverbatim
 *>
 *> \param[in] IRESID
@@ -225,7 +226,7 @@ DOUBLE PRECISION FUNCTION ZQRT17( TRANS, IRESID, M, N, NRHS, A,
      $                INFO )
       END IF
 *
-*     compute R'*op(A)
+*     compute R**H * op(A)
 *
       CALL ZGEMM( 'Conjugate transpose', TRANS, NRHS, NCOLS, NROWS,
      $            DCMPLX( ONE ), C, LDB, A, LDA, DCMPLX( ZERO ), WORK,
diff --git a/TESTING/LIN/ztbt02.f b/TESTING/LIN/ztbt02.f
index fdfa35e6be..9943d94672 100644
--- a/TESTING/LIN/ztbt02.f
+++ b/TESTING/LIN/ztbt02.f
@@ -53,9 +53,9 @@
 *> \verbatim
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to A.
-*>          = 'N':  A *x = b     (No transpose)
-*>          = 'T':  A**T *x = b  (Transpose)
-*>          = 'C':  A**H *x = b  (Conjugate transpose)
+*>          = 'N':  A    * X = B  (No transpose)
+*>          = 'T':  A**T * X = B  (Transpose)
+*>          = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] DIAG
@@ -142,7 +142,7 @@
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
 *>          The maximum over the number of right hand sides of
-*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *> \endverbatim
 *
 *  Authors:
@@ -204,7 +204,7 @@ SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
          RETURN
       END IF
 *
-*     Compute the 1-norm of A or A'.
+*     Compute the 1-norm of op(A).
 *
       IF( LSAME( TRANS, 'N' ) ) THEN
          ANORM = ZLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
@@ -221,7 +221,7 @@ SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
       END IF
 *
 *     Compute the maximum over the number of right hand sides of
-*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
+*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
 *
       RESID = ZERO
       DO 10 J = 1, NRHS