Let $f$ and $g$ linear operators in $V$ which are both diagonalizables. We say that $f$ and $g$ are simultaneously diagonalizables if there exists a basis $\alpha$ of $V$ in which both $\mathop {\left[f\right]} \nolimits_\alpha ^\alpha$ as $\left[ g \right]_\alpha ^\alpha $ are diagonal matrices. Prove that $f$ and $g$ are simultaneously diagonalizables if and only if $f$ and $g$ commute.
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https://math.stackexchange.com/questions/236212/simultaneously-diagonalizable-proof?rq=1 – Elle Najt May 13 '18 at 17:19
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This is in all the linear algebra books.... – Angina Seng May 13 '18 at 17:20