Factoring Permutation Matrices Into a Product of Tridiagonal Matrices
classification
🧮 math.CO
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.
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