Hi Ravi, Thank you for your useful reply. Does the result also hold for variance-covariance matrices that have one or more zero eigenvalues? Do you have a reference to suggest?
Thank you again! Giovanni > Date: Tue, 15 Apr 2008 18:14:11 -0400 > From: Ravi Varadhan <[EMAIL PROTECTED]> > Thread-index: AcifQeEz9B1geo3TQyesYlQGMCSuNgAAWF1QAACa9sA= > > 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: [EMAIL PROTECTED] > > Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html > > > > ---------------------------------------------------------------------------- > -------- > > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > Behalf Of Ravi Varadhan > Sent: Tuesday, April 15, 2008 6:03 PM > To: 'Giovanni Petris'; r-help@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: [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. > ______________________________________________ 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.
