> -----Original Message----- > From: [email protected] [mailto:r-help-bounces@r- > project.org] On Behalf Of Jie > Sent: Tuesday, July 31, 2012 2:23 PM > To: [email protected] > Subject: [R] about changing order of Choleski factorization and inverse > operation of a matrix > > Dear All, > > My question is simple but I need someone to help me out. > Suppose I have a positive definite matrix A. > The funtion chol() gives matrix L, such that A = L'L. > The inverse of A, say A.inv, is also positive definite and can be > factorized as A.inv = M'M. > Then > A = inverse of (A.inv) = inverse of (M'M) = (inverse of M) %*% > (inverse of M)' > = ((inverse of M)')'%*% (inverse of M)', > i.e. if define B = transpose of (inverse of M), then A = B' %*% B. > Therefore L = B = transpose of (inverse of M) = transpose of (inverse > of > chol(A.inv)) > But when I try it in R, the answer is not as expected. > > code as below: > > A <- matrix(1:9,3,3) > A <- A + t(A) > diag(A) <- 50 > print(A) > L <- chol(A) > B <- t(solve(chol(solve(A)))) > print(L) > print(B) > > Thank you in advance, > > Best wishes, > Jie >
This is not an R question, it is a question about your understanding of matrix algebra. Just because L'L == B'B does not mean that L must equal B. You have your own counter-example. Just take your calculated L and B matrices and compute t(L) %*% L and t(B) %*% B or all.equal((t(L) %*% L ) , (t(B) %*% B)) Hope this is helpful, Dan Daniel J. Nordlund Washington State Department of Social and Health Services Planning, Performance, and Accountability Research and Data Analysis Division Olympia, WA 98504-5204 ______________________________________________ [email protected] 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.
