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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. $K_m = V_m \Lambda_m V_m^T$?

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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 $A$.

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  • $\begingroup$ You should probably have a look to the link given by Suvrit in comment to the question. $\endgroup$
    – Benoît Kloeckner
    Commented Apr 26, 2014 at 21:00

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