2015/10/26 by Muhammad El Gebali, Gebali, Muhammad El, Nermine El-Sissi +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1510.07675
13 pages, 3 figures
arxiv created 2015/10/26 · openalex publication_date 2015/10/26 · arxiv updated 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.