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Let $A,B:E\to E$, where $E$ is a finite dimensional vector space, be two linear operators such that all of the eigenvalues are real numbers.

If $AB=BA$, prove that there exists a basis in which both the matrices of $A$ and $B$ are triangular.

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  • $\begingroup$ See this post for one approach $\endgroup$ – Omnomnomnom May 20 at 6:05
  • $\begingroup$ Also, what have you tried? What are your thoughts on the problem? $\endgroup$ – Omnomnomnom May 20 at 6:05

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