If its not important which of many solutions you use then the generalized inverse can be used, say. Just use 0 for each small eigenvalue and 1/sqrt(x) for the others.
On Mon, Aug 10, 2009 at 6:36 PM, cindy Guo<cindy.g...@gmail.com> wrote: > Hi, Ted, > > Thanks for the sample code. It is exactly what I want. But can I ask another > question? The matrix for which I want the negative square root is a > covariance matrix. I suppose it should be positive definite, so I can do > 1/sqrt(V) as you wrote. But the covariance matrix I got in R using the > function cov has a lot of negative eigenvalues, like -5.338634e-17, so > 1/sqrt(V) generates NA's. Can you tell what's the problem here. > > Thanks, > Cindy > > On Mon, Aug 10, 2009 at 2:53 PM, Ted Harding > <ted.hard...@manchester.ac.uk>wrote: > >> On 10-Aug-09 21:31:30, cindy Guo wrote: >> > Hi, All, >> > If I have a symmetric matrix, how can I get the negative square root >> > of the matrx, ie. X^(-1/2) ? >> > >> > Thanks, >> > >> > Cindy >> >> X <- matrix(c(2,1,1,2),nrow=2) >> X >> # [,1] [,2] >> # [1,] 2 1 >> # [2,] 1 2 >> >> E <- eigen(X) >> V <- E$values >> Q <- E$vectors >> Y <- Q%*%diag(1/sqrt(V))%*%t(Q) >> Y >> # [,1] [,2] >> # [1,] 0.7886751 -0.2113249 >> # [2,] -0.2113249 0.7886751 >> >> solve(Y%*%Y) ## i.e. find its inverse >> # [,1] [,2] >> # [1,] 2 1 >> # [2,] 1 2 >> >> Hence (Y%*%Y)^(-1) = X, or Y = X^(-1/2) >> >> Hopingb this helps, >> Ted. >> >> -------------------------------------------------------------------- >> E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> >> Fax-to-email: +44 (0)870 094 0861 >> Date: 10-Aug-09 Time: 22:53:25 >> ------------------------------ XFMail ------------------------------ >> > > [[alternative HTML version deleted]] > > ______________________________________________ > 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.
