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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See this post for one approach – Ben Grossmann May 20 '19 at 06:05
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Also, what have you tried? What are your thoughts on the problem? – Ben Grossmann May 20 '19 at 06:05