If I have A and B, both nxn, with eigenvalues a and b respectively, will a-b be an eigenvalue of the matrix A-B?
2026-04-05 14:05:27.1775397927
Are the eigenvalues of a matrix sum the same as the sum of the eigenvalues of individual matrices?
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No unless they share eigenvectors. If $\vec v$ is an eigenvector of both $A$ and $B$, $$A\vec v=a\vec v\\B\vec v=b\vec v$$Then $$(A-B)\vec v=(a-b)\vec v$$so $a-b$ is an eigenvalue of the matrix. If they do not share the same eigenspaces, then you cannot guarantee that this will be an eigenvalue (it still can be, but you can't tell in general).