# [R] geodesic distance (solution)

From: stefano iacus <stefano.iacus_at_unimi.it>
Date: Fri 04 Aug 2006 - 17:14:09 EST

> 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

I'm pretty sure that the problem can also be solved using some svd decomposition when B is not invertible.

hope it helps
stefano

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