Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

Details Factoring Permutation Matrices Into a Product of Tridiagonal Matrices Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

2010-07-20

arxiv.org/abs/1007.3467v1

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

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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