diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index cbbae8e852b2e..3816ee926dead 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -559,7 +559,9 @@ end
 """
     strides(A)
 
-Return a tuple of the memory strides in each dimension.
+Return a tuple of the memory strides in each dimension, for an `AbstractArray` with a
+strided memory layout. For arrays with a non-strided layout (such as sparse arrays), return
+`nothing`.
 
 See also: [`stride`](@ref).
 
@@ -571,7 +573,7 @@ julia> strides(A)
 (1, 3, 12)
 ```
 """
-function strides end
+strides(::AbstractArray) = nothing
 
 """
     stride(A, k::Integer)
@@ -592,15 +594,14 @@ julia> stride(A,3)
 ```
 """
 function stride(A::AbstractArray, k::Integer)
-    st = strides(A)
-    k ≤ ndims(A) && return st[k]
-    ndims(A) == 0 && return 1
-    sz = size(A)
-    s = st[1] * sz[1]
-    for i in 2:ndims(A)
-        s += st[i] * sz[i]
+    str = strides(A)
+    if str === nothing
+        return nothing
+    else
+        k ≤ ndims(A) && return st[k]
+        ndims(A) == 0 && return 1
+        return sum(st .* size(A))
     end
-    return s
 end
 
 @inline size_to_strides(s, d, sz...) = (s, size_to_strides(s * d, sz...)...)
diff --git a/base/permuteddimsarray.jl b/base/permuteddimsarray.jl
index cf9748168aac2..acf1c364fb7fb 100644
--- a/base/permuteddimsarray.jl
+++ b/base/permuteddimsarray.jl
@@ -61,7 +61,11 @@ Base.pointer(A::PermutedDimsArray, i::Integer) = throw(ArgumentError("pointer(A,
 
 function Base.strides(A::PermutedDimsArray{T,N,perm}) where {T,N,perm}
     s = strides(parent(A))
-    ntuple(d->s[perm[d]], Val(N))
+    if s === nothing
+        return nothing
+    else
+        return ntuple(d->s[perm[d]], Val(N))
+    end
 end
 Base.elsize(::Type{<:PermutedDimsArray{<:Any, <:Any, <:Any, <:Any, P}}) where {P} = Base.elsize(P)
 
diff --git a/stdlib/LinearAlgebra/src/adjtrans.jl b/stdlib/LinearAlgebra/src/adjtrans.jl
index b722e49bb2c3d..5281dba7e6e8f 100644
--- a/stdlib/LinearAlgebra/src/adjtrans.jl
+++ b/stdlib/LinearAlgebra/src/adjtrans.jl
@@ -382,6 +382,25 @@ parent(A::AdjOrTrans) = A.parent
 vec(v::TransposeAbsVec{<:Number}) = parent(v)
 vec(v::AdjointAbsVec{<:Real}) = parent(v)
 
+# provide strides, but only for eltypes that are directly stored in memory (i.e. unaffected
+# by recursive `adjoint` and `transpose`, being `Real` and `Number` respectively)
+function Base.strides(a::Union{Adjoint{<:Real, <:AbstractVector}, Transpose{<:Number, <:AbstractVector}})
+    str = strides(a.parent)
+    if str === nothing
+        return nothing
+    else
+        return (1, str[1])
+    end
+end
+function Base.strides(a::Union{Adjoint{<:Real, <:AbstractMatrix}, Transpose{<:Number, <:AbstractMatrix}})
+    str = strides(a.parent)
+    if str === nothing
+        return nothing
+    else
+        return (str[2], str[1])
+    end
+end
+
 ### concatenation
 # preserve Adjoint/Transpose wrapper around vectors
 # to retain the associated semantics post-concatenation