The eigenvalues are the squares of the singular values (although you need to watch the scalings used, in particular n vs n-1). (This is standard theory.)
Since both are non-negative, given one you can get the other. On Tue, 2 Aug 2005, Sundar Dorai-Raj wrote: > > > Rebecca Young wrote: >> Hello, >> >> Can you get eigenvalues in addition to eigevectors using prcomp? If so how? >> I am unable to use princomp due to small sample sizes. >> Thank you in advance for your help! >> Rebecca Young >> > > > Hi, Rebecca, > > From ?prcomp: > > The calculation is done by a singular value decomposition of the > (centered and possibly scaled) data matrix, not by using 'eigen' > on the covariance matrix. This is generally the preferred method > for numerical accuracy. ... > > So you can get the singular values, but not the eigenvalues. You could > use ?princomp if you really want the eigenvalues. In either case, you > read the code to see how this is done. > > x <- matrix(rnorm(1000), 100, 10) > > # eigenvalues > v <- cov.wt(x) > ev <- eigen(v$cov * (1 - 1/v$n.obs), symmetric = TRUE)$values > ev[ev < 0] <- 0 > princomp(x)$sdev > sqrt(ev) > > # singular values > sv <- svd(scale(x, center = TRUE, scale = FALSE), nu = 0) > prcomp(x)$sdev > sv$d/sqrt(max(1, nrow(x) - 1)) > > HTH, > > --sundar > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html