Original scientific paper

https://doi.org/10.3336/gm.53.1.05

A combinatorial interpretation of the LDU-decomposition of totally positive matrices and their inverses

Muhammad ElGebali orcid.org/0000-0001-5690-1009 ; Mathematics and Actuarial Science Department, The American University in Cairo, 11 853 Cairo, Egypt
Nermine El-Sissi ; Mathematics and Actuarial Science Department, The American University in Cairo, 11 853 Cairo, Egypt

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 Fomin and Zelevinsky [5]. 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.

Keywords

Totally positive matrices; LDU factorization; planar networks

Hrčak ID:

201812

URI

https://hrcak.srce.hr/201812

Publication date:

20.6.2018.

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