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[bug-gsl] Re: Definition of Singular Value Decomposition (2008-09-05)

From: Brian Gough <bjg@gnu.org>
Subject: Re: Definition of Singular Value Decomposition
Date: Fri, 05 Sep 2008 18:03:27 +0100
To: "Geelen Bert" <bgeelen@.......>
Cc: bug-gsl@gnu.org

At Wed, 3 Sep 2008 15:51:12 +0200,
Geelen Bert wrote:
> Shouldn't the dimensions of U and S instead be as follows:
> "A general rectangular M-by-N matrix A has a singular value
> decomposition (svd) into the product of an M-by-M orthogonal matrix U,
> an M-by-N diagonal matrix of singular values S and the transpose of an
> N-by-N orthogonal square matrix V"

Thanks for your email. The routines compute the "thin" version of the
SVD as opposed to the "full" SVD. I will add a note to the manual to
make that clearer.

--
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/