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Subject: Re: SVD which one is which
Date: Fri, 26 Dec 2008 23:21:02 +0000 (UTC)
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"Ali Saleemi" <naumansaleemi@hotmail.com> wrote in message <gj3n2r\$akd\$1@fred.mathworks.com>...
> 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."

http://en.wikipedia.org/wiki/Singular_value_decomposition#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

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