Document SingularException throw for inv(::AbstractMatrix)

[Antoinemarteau]

I suggest documenting that inv(::AbstractMatrix) throws on (numerically) singular matrices, this is different from inv(::Number) that returns Inf.

inv( 0. )    # Inf, no exception
inv( [0;;] ) # SingularException 

I guess documenting this would mean that inv guarantees to return a matrix with only finite (isfinite) entries if the argument has only finite entries, but I don't know if the implementation guarantees it / if this should be tested ?

[Antoinemarteau]

Also, inv(M) where M = [Nan;;] currently returns [Nan;;], but then M*inv(M) == Matrix(I,1,1) is false, so what is returned isn't an inverse and the documentation doesn't specify it.

Should this be also documented, or fixed to throw a SingularExcteption ? On one hand [Nan;;] do not have a zero eigenvalue like SingularException says, but it isn't invertible either.

Other inconsistencies with NaN:

julia> M = [NaN 1; 1 0;]

julia> inv(M) 
ERROR: ArgumentError: matrix contains Infs or NaNs
... 

julia> M = [NaN 0; 0 1;]

julia> inv(M)
2×2 Matrix{Float64}:
 NaN    NaN
   0.0    1.0

julia> Matrix(I,2,2) == inv(M)*M
false

[ViralBShah]

Welcome @Antoinemarteau !

[codecov]

Codecov Report

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##           master    #1331      +/-   ##
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- Coverage   93.76%   93.74%   -0.03%     
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  Lines       15751    15751              
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