Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

Abstract

Gilbert Strang posited that a permutation matrix of bandwidth $w$ can be written as a product of $N<2w$ permutation matrices of bandwidth 1. A proof employing a greedy ``parallel bubblesort'' algorithm on the rows of the permutation matrix is detailed and further points of interest are elaborated.

11 pages, 1 figure