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arXiv · 1007.3467

Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

Michael Daniel Samson·Martianus Frederic Ezerman
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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.

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Michael Daniel Samson, Martianus Frederic Ezerman. 2010-07-20. Factoring Permutation Matrices Into a Product of Tridiagonal Matrices. https://arxiv.org/abs/1007.3467

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