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: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Giovanni Petris Sent: Tuesday, April 15, 2008 5:43 PM To: r-help@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 <[EMAIL PROTECTED]> Associate Professor Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.