#### Title

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