>that it's SVD is equivalent to the GESVD LAPACK routine.
The comment was meant for the ILinearAlgebra interface and probably shouldn't have been copied to the managed code implementation. I'll remove it in both places to prevent future confusion.
>What is the difference between LAPACK GESVD and LAPACK DGESVD?
DGESVD is the double precision version of GESVD, SGESVD is the single precision, and so on.
SVD is only unique up to to the sign (for real numbers, I think it is a little more complicated for complex numbers). From a quick search it seems that LAPACK uses QR decomp to compute the SVD while LINPACK uses Lanczos iterations. That probably explains the
differences in signs.