Excellent, thanks that is very helpful!

Thanks. Yes I came across Horn's stuff. So is this related because if you exponentiate the matrices it is addition of exponents as in the paper?

:) If only it were that easy. Unfortunately a general diagonal matrix will change the eigenvalues and eigenvectors... It seems like there should be a way to update the eigendecomposition but I'm stumped. This is for an implementation of Gaussian belief propagation. First mathoverflow question--thanks for your thoughts.