Let V a a finite dimensional vector space over a field $K$ and let $S, T ~\in~ End(V)$ both diagonalizable and that $[S, T] = 0$. Show that $S, T$ are simultaneously diagonalizable. I've tried to show that $V_{\lambda}$ is $S-stable$ by descomposing $V = \oplus_{\lambda \in Spec(T)} $ but I get nowhere. Thank you all in advance
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this and every variation of it is done in the first Horn and Johnson book. – Will Jagy May 06 '20 at 18:11
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Possible duplicate of https://math.stackexchange.com/questions/236212/prove-that-simultaneously-diagonalizable-matrices-commute – Jan May 06 '20 at 19:20
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Thanks, I didn´t see those. – May 06 '20 at 19:45