MATRICES THAT COMMUTE WITH A PERMUTATION MATRIX
Let P be an n x n permutation matrix, and let p be the corresponding permutation. Let A be a matrix such that AP = PA. It is well known that when p is an n-cycle, A is permutation similar to a circulant matrix. We present results for the band patterns in A and for the eigenstructure of A when p consists of several disjoint cycles. These results depend on the greatest common divisors of pairs of cycle lengths.
LINEAR ALGEBRA AND ITS APPLICATIONS
(1991). MATRICES THAT COMMUTE WITH A PERMUTATION MATRIX. LINEAR ALGEBRA AND ITS APPLICATIONS, 150, 255-265.
Available at: http://aquila.usm.edu/fac_pubs/6965