Make pinv work for Adjoint (#29837)

Fixes #29723

(cherry picked from commit a472bc7)

Author: andreasnoack

stdlib/LinearAlgebra/src/dense.jl

@@ -1262,7 +1262,7 @@ julia> M * N
 
 [^KY88]: Konstantinos Konstantinides and Kung Yao, "Statistical analysis of effective singular values in matrix rank determination", IEEE Transactions on Acoustics, Speech and Signal Processing, 36(5), 1988, 757-763. [doi:10.1109/29.1585](https://doi.org/10.1109/29.1585)
 """
-function pinv(A::StridedMatrix{T}, rtol::Real) where T
+function pinv(A::AbstractMatrix{T}, rtol::Real) where T
     m, n = size(A)
     Tout = typeof(zero(T)/sqrt(one(T) + one(T)))
     if m == 0 || n == 0
@@ -1291,7 +1291,7 @@ function pinv(A::StridedMatrix{T}, rtol::Real) where T
     Sinv[findall(.!isfinite.(Sinv))] .= zero(Stype)
     return SVD.Vt' * (Diagonal(Sinv) * SVD.U')
 end
-function pinv(A::StridedMatrix{T}) where T
+function pinv(A::AbstractMatrix{T}) where T
     rtol = eps(real(float(one(T))))*min(size(A)...)
     return pinv(A, rtol)
 end

stdlib/LinearAlgebra/test/dense.jl

@@ -87,6 +87,9 @@ bimg  = randn(n,2)/2
             pinva15 = pinv(a[:,1:n1])
             @test a[:,1:n1]*pinva15*a[:,1:n1] ≈ a[:,1:n1]
             @test pinva15*a[:,1:n1]*pinva15 ≈ pinva15
+            pinva15 = pinv(a[:,1:n1]') # the Adjoint case
+            @test a[:,1:n1]'*pinva15*a[:,1:n1]' ≈ a[:,1:n1]'
+            @test pinva15*a[:,1:n1]'*pinva15 ≈ pinva15
 
             @test size(pinv(Matrix{eltya}(undef,0,0))) == (0,0)
         end