Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

Martianus Frederic Ezerman; Michael Daniel Samson

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Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

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arxiv 1007.3467 v1 pith:AB4V6B74 submitted 2010-07-20 math.CO

Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

Michael Daniel Samson , Martianus Frederic Ezerman This is my paper

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keywords permutationmatricesbandwidthmatrixproductalgorithmbubblesortdetailed

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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.

Factoring Permutation Matrices Into a Product of Tridiagonal Matrices

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