Glasnik matematički, Vol. 53 No. 1, 2018.
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
Publication date:
20.6.2018.
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