Re: [R] SVD of a variance matrix

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Tue, 15 Apr 2008 18:14:11 -0400

Let me correct my reply a bit.

U and V will differ by a factor of (-1) corresponding to negative eigenvalues (if any) of a general symmetric A. However, for symmetric positive-definite matrices (e.g. variance-covariance matrix), they will be identical.

Ravi.



Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan_at_jhmi.edu

Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html  



-----Original Message-----

From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of Ravi Varadhan
Sent: Tuesday, April 15, 2008 6:03 PM
To: 'Giovanni Petris'; r-help_at_r-project.org Subject: Re: [R] SVD of a variance matrix

Yes. SVD of any symmetric (which is, of course, also square) matrix will always have U = V. Also, SVD is the same as spectral decomposition, and the columns of U and V are the eigenvectors, but the singular values will be the absolute value of eigenvalues.

Ravi.



Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan_at_jhmi.edu

Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html  



-----Original Message-----

From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of Giovanni Petris
Sent: Tuesday, April 15, 2008 5:43 PM
To: r-help_at_r-project.org
Subject: [R] SVD of a variance matrix

Hello!

I suppose this is more a matrix theory question than a question on R, but I will give it a try...

I am using La.svd to compute the singular value decomposition (SVD) of a variance matrix, i.e., a symmetric nonnegative definite square matrix. Let S be my variance matrix, and S = U D V' be its SVD. In my numerical experiments I always got U = V. Is this necessarily the case? Or I might eventually run into a SVD which has U != V?

Thank you in advance for your insights and pointers.

Giovanni

-- 

Giovanni Petris  <GPetris_at_uark.edu>
Associate Professor
Department of Mathematical Sciences
University of Arkansas - Fayetteville, AR 72701
Ph: (479) 575-6324, 575-8630 (fax)
http://definetti.uark.edu/~gpetris/

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Received on Tue 15 Apr 2008 - 22:22:02 GMT

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