> Hi,
> has anyone ever seen implemented in R the following "geodesic"
> distance between positive definite pxp matrices A and B?
>
> d(A,B) = \sum_{i=1}^p (\log \lambda_i)^2
>
> were \lambda is the solution of det(A -\lambda B) = 0
>
> thanks
> stefano
as I received few private email on the claimed solution, I'm posting
it to r-help.
when matrix B is invertible (which is always my case), one approach
is to notice that
solving
det(A -\lambda * B) = 0
is equivalent to solve
det(B^-1*A -\lambda *I) = 0
which is a standard eigen value problem for the matrix B^-1 * A, hence
eigen(solve(B) %*% A)$values
is the answer.
I'm pretty sure that the problem can also be solved using some svd
decomposition when B is not invertible.
hope it helps
stefano