I gave you a solution for the triangular matrix. Can you explain why that is not what you need?
> -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of Shawn Koppenhoefer > Sent: Tuesday, April 12, 2011 11:37 AM > To: r-help@r-project.org > Subject: Re: [R] B %*% t(B) = R , then solve for B > Importance: High > > BTW, > The same solution can be found using SVD (Singular Value Decomposition) > > example, > > ## Define the matrix that we want to decompose into the product of a > matrix and its transform > M<-matrix(c(0.6098601, 0.2557882, 0.1857773, > 0.2557882, 0.5127065, -0.1384238, > 0.1857773, -0.1384238, 0.9351089 ), > nrow=3, ncol=3, byrow=TRUE) > > ## Compute the singular-value decomposition, and construct F from its pieces > SVD=svd(M, nu=3, nv=3) > U=SVD$u > D=diag(SVD$d) > V=SVD$v > U %*% D %*% t(V) > F = U %*% sqrt(diag(SVD$d)) > > ## Test to see of the product of F with its transpose is equal to M > F %*% t(F) # > [,1] [,2] [,3] > [1,] 0.6098601 0.2557882 0.1857773 > [2,] 0.2557882 0.5127065 -0.1384238 > [3,] 0.1857773 -0.1384238 0.9351089 > > > /Shawn > > > p.s. > HOWEVER I would still like to find a solution that gives me a diagonal > matrix for F. > For example, I would like this result:, > > > F > [,1] [,2] [,3] > [1,] 0.781 0.000 0.000 > [2,] 0.328 0.637 0.000 > [3,] 0.238 -0.341 0.873 > > > > [[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.
