# Re: question on the svd

**From:** Jentje Goslinga (*goslinga_at_telus.net*)

**Date:** 12/16/04

**Next message:**Jentje Goslinga: "Re: small numerical differences in floating point result between wintel and Sun/SPARC"**Previous message:**Tim Prince: "Re: small numerical differences in floating point result between wintel and Sun/SPARC"**In reply to:**rm: "question on the svd"**Next in thread:**Ian Bush: "Re: question on the svd"**Reply:**Ian Bush: "Re: question on the svd"**Reply:**Gordon Sande: "Re: question on the svd"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Date: Thu, 16 Dec 2004 07:00:45 GMT

rm wrote:

* > I read that for a non-square matrix, A, eg: mxn, m<n only the
*

* > singular values D are unique. A = U*D*V'
*

* >
*

* > And that A can be expressed as: A = U1*D*V1' = U2*D*V2'
*

* >
*

* > How does one compute different possibilities of the left and right
*

* > singular matrices ie the set of {U} and the set of {D}? and the
*

* > number of solutions that exist in the set?
*

This is not so mysterious, you can work minus signs into

both the left and right matrices by writing

D = Ik.D.Ik

with Ik a Unit Matrix with its k-th diagonal element negated.

Now left multiply Ik into V' and right multiply into U.

Work out for yourself in how many ways this can be done.

This is not really any different from the symmetric eigenvalue

problem where eigenvectors are also determined up to a

multiplication by -1.

The folks in sci.math.num-analysis probably can say it better.

* > Thanks!
*

Jentje Goslinga

**Next message:**Jentje Goslinga: "Re: small numerical differences in floating point result between wintel and Sun/SPARC"**Previous message:**Tim Prince: "Re: small numerical differences in floating point result between wintel and Sun/SPARC"**In reply to:**rm: "question on the svd"**Next in thread:**Ian Bush: "Re: question on the svd"**Reply:**Ian Bush: "Re: question on the svd"**Reply:**Gordon Sande: "Re: question on the svd"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]