Apologies if this is too basic, but given a permutation matrix $M$, is there any parameter or formula based on $M$ that gives the disjoint cycle decomposition, or at least the conjugacy class, of the corresponding permutation?
Conjugacy class of a permutation from its matrix representation
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matrices
permutations
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0If you actually want to find a cycle decomposition, this probably isn't the way to do it. What is the intended application? – 2011-02-15
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0@Qiaochu Yuan: I know. I'm not actually interested in finding the dcd, I just want to prove a relation between two different constructions and it seems that expressing permutations as matrices may make things easier in this case. – 2011-02-15