Giovanni, Both matrices describing the points (A and B in my example) are the same size, so the resulting matrix will always be square. Also, the equation I'm using is essentially the following identity:
Var(A + B) = Var(A) + Var(B) + Cov(A, B) + Cov(B, A) All the covariance matrices that result from the Var() terms should be positive definite, and while it seems possible that either of those resulting from the Cov() terms may not be, the sum of the two should. Do you agree? Of course, the above identity only holds if the data is normally distributed. The Mardia test for multivariate normality in fact shows that my data is not. This may ultimately be my problem. So maybe I should be asking if you could point me toward some packages that can transform my data so that it is normally distributed. - Jeff On Mon, Nov 15, 2010 at 3:56 PM, Giovanni Petris <gpet...@uark.edu> wrote: > What made you think that a cross-covariance matrix should be positive > definite? Id does not even need to be a square matrix, or symmetric. > > Giovanni Petris > > On Mon, 2010-11-15 at 12:58 -0500, Jeff Bassett wrote: >> I am creating covariance matrices from sets of points, and I am having >> frequent problems where I create matrices that are non-positive >> definite. I've started using the corpcor package, which was >> specifically designed to address these types of problems. It has >> solved many of my problems, but I still have one left. >> >> One of the matrices I need to calculate is a cross-covariance matrix. >> In other words, I need to calculate cov(A, B), where A and B are each >> a matrix defining a set of points. The corpcor package does not seem >> to be able to perform this operation. >> >> Can anyone suggest a way to create cross-covariance matrices that are >> guaranteed (or at least likely) to be positive definite, either using >> corpcor or another package? >> >> I'm using R 2.8.1 and corpcor 1.5.2 on Mac OS X 10.5.8. >> >> - Jeff >> >> ______________________________________________ >> 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.