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I was wondering if there is a way to generate a permutation matrix P such that each application of P to another matrix A will find the "next" permutation of A. I'm looking for a way to generate a permutation matrix P (size m x m) such that applying it m! times to A (m x m) returns A (after having rolled through all possible permutations of A).

Am I looking for something I'm not going to be able to find?

Thanks!