Eigendecomposition of a summation of matrices

Question

Can anyone tell me if there's a way to relate the eigendecomposition of the result of a summation of matrices with the eigendecomposition of those matrices? More specifically: If I have a matrix $K = \sum\limits_{m=1}^M a_m K_m$, $a_m \in R$.

How can I relate its eigendecomposition, $K = V \Lambda T^T$, with the eigendecomposition of the matrices in the summation, i.e. $K_m = V_m \Lambda_m V_m^T$?

score 1 · Answer 1 · answered Apr 26 '14 at 19:52

1

There is nothing useful to say. Consider the decomposition $I=A+(I-A)$. There is no useful relation between the eigenvalues of $I$ and those of $A$.

answered Apr 26 '14 at 19:52

Chris Godsil

12,043

You should probably have a look to the link given by Suvrit in comment to the question. – Benoît Kloeckner Apr 26 '14 at 21:00

Eigendecomposition of a summation of matrices

1 Answers1