Factoring Permutation Matrices Into a Product of Tridiagonal Matrices
Combinatorics
2010-07-21 v1
Abstract
Gilbert Strang posited that a permutation matrix of bandwidth can be written as a product of 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.
Keywords
Cite
@article{arxiv.1007.3467,
title = {Factoring Permutation Matrices Into a Product of Tridiagonal Matrices},
author = {Michael Daniel Samson and Martianus Frederic Ezerman},
journal= {arXiv preprint arXiv:1007.3467},
year = {2010}
}
Comments
11 pages, 1 figure