As part of a larger problem involving classifying intertwining operators of two group representations, I came across the following question: If [itex]X[/itex] is an [itex]n \times n[/itex] diagonal matrix with [itex]n[/itex] distinct non-zero eigenvalues, then exactly which [itex]n \times n[/itex] matrices [itex]A[/itex] satisfy the following equality [itex]AXA^{-1} = X[/itex]? Does anyone know the answer to this question?(adsbygoogle = window.adsbygoogle || []).push({});

Edit: Nevermind. I found a better way of doing the problem that avoids this sort of argument.

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# Similar Diagonal Matrices

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