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Newsgroups: comp.soft-sys.matlab
Subject: Re: SVD which one is which
Date: Fri, 26 Dec 2008 23:21:02 +0000 (UTC)
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"Ali Saleemi" <> wrote in message <gj3n2r$akd$>...
> SVD gives eigenvectors in descending order, is there anyway to know which eigen vector belongs to which variable in the original matrix?  I dont have a square matrix in my original data so I cannot use eig() which according to my knowledge does not sort the eigenvectors.
> .......

  I refer you to the Wikipedia website for a discussion on singular value decompositions.  In particular read the section entitled "Relation to eigenvalue decomposition."

  In answer to your question "which eigen vector belongs to which variable in the original matrix", there is no such relationship.  There is a relationship in the pairings between eigenvalues and eigenvectors, which is a different concept.  When matlab's 'svd' does give an eigenvalue decomposition, the pairing is between the eigenvalues of S and the corresponding columns of V in the decomposition

 M = U*S*V';

Roger Stafford