Does a diagonal matrix commute with every other matrix of the same size?
I'm stuck on one line of a proof that I am writing, and I would like to switch order between a non-diagonal and a diagonal matrix.
Thanks,
2026-03-28 20:57:28.1774731448
Does a diagonal matrix commute with every other matrix of the same size?
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In general, a diagonal matrix does not commute with another matrix. You can find simple counterexamples in the comments. For a matrix to commute with all the others you need the matrix to be scalar, i.e. diagonal with entries on the diagonal which are all the same.