Title

Matrices That Commute With a Permutation Matrix

Document Type

Article

Publication Date

5-1-1991

Department

Mathematics

Abstract

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.

Publication Title

Linear Algebra and Its Applications

Volume

150

First Page

255

Last Page

265