If $A,B$ are diagonalizable complex matrices of size $n$ such that $AB=BA$ , then is there a common eigen-basis of $A$ and $B$ ?
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1First prove the following: If $AB = BA$, then each eigenspace of $A$ is preserved by $B$. – Amritanshu Prasad Nov 09 '14 at 16:15
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1Yes. Have a look at: http://math.stackexchange.com/questions/6258/matrices-commute-common-basis-of-eigenvectors – Simon S Nov 09 '14 at 16:29