Matrices That Commute With a Permutation Matrix
Document Type
Article
Publication Date
5-1-1991
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
Let P be an n×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
Recommended Citation
Stuart, J. L.,
Weaver, J. R.
(1991). Matrices That Commute With a Permutation Matrix. Linear Algebra and Its Applications, 150, 255-265.
Available at: https://aquila.usm.edu/fac_pubs/6965