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arXiv · 1510.07675

A Combinatorial Interpretation of the LDU Decomposition of Totally Positive Matrices

Muhammad El Gebali·Nermine El-Sissi
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Abstract

We study the combinatorial description of the LDU decomposition of totally positive matrices. We give a description of the lower triangular L, the diagonal D, and the upper triangular U matrices of the LDU decomposition of totally positive matrices in terms of the combinatorial structure of essential planar networks described by Zelvinsky and Fomin. Similarly, we find a combinatorial description of the inverses of these matrices. In addition, we provide recursive formulae for computing the L, D, and U matrices of a totally positive matrix.

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Muhammad El Gebali, Nermine El-Sissi. 2015-10-26. A Combinatorial Interpretation of the LDU Decomposition of Totally Positive Matrices. https://arxiv.org/abs/1510.07675

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