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From: Greg Heath <heath@alumni.brown.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: SVD which one is which
Date: Sat, 27 Dec 2008 09:43:47 -0800 (PST)
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On Dec 26, 5:50 pm, "Ali Saleemi" <naumansale...@hotmail.com> wrote:
> SVD gives eigenvectors in descending order, is there
> anyway to know which eigen vector belongs to which
> variable in the original matrix?

In general, SVD and SVDS yields singular vectors of A,
not eigenvectors of A. The  nonnegative real singular
values and corresponding singular vectors are
ordered w.r.t ascending singular values in SVD.
I am not sure about the ordering in SVDS..

doc SVD
dov SVDS

In general, each singular vector is a linear combination of
all the variables. In real-world-problems, it is rare that
singular vectors are coordinate aligned.

The singular vectors of A are eigenvectors of
A*A^T and A^T*A.

> 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.

If A is square, both EIG and EIGS  yield eigenvectors
of A.  If A is symmetric, the eigenvalues are real and the
corresponding eigenvectors are sorted (ascending for EIG
and descending for EIGS).

doc EIG
doc EIGS

Hope this helps.

Greg