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nomadreid

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- Beyond fixed points and transpositions, is there an easy way to spot the subset of rows in a permutation matrix that indicate a cycle ?

In a permutation matrix (the identity matrix with rows possibly rearranged), it is easy to spot those rows which will indicate a fixed point -- the one on the diagonal -- and to spot the pairs of rows that will indicate a transposition: a pair of ones on a backward diagonal, i.e., where the row+column subscripts are a constant -- and of course one can find cycles by multiplying a vector and tracing around what goes to what. But is there some quicker way to spot the collections of rows that will correspond to a cycle?