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Let's consider a set of $m$ generic square matricies $(N;N) $ defined on $R$ which forms a group. Chosen one of these $ m $ matrices, I know that, by changing the base on my vectorial space, I can obtain a diagonal matrix or at least a matrix in a Jordan form. My question is, does exist a particular change of basis rapresented by the matrix $T$, which diagonalizes or puts in Jordan form all the matrices of the group? If so, how is this matrix $T$?

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  • $\begingroup$ I think at least the group should be Abelian. $\endgroup$ – xbh Nov 24 '18 at 16:57

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