P-matrices and signed digraphs
Combinatorics
2010-06-02 v1
Abstract
We associate a signed digraph with a list of matrices whose dimensions permit them to be multiplied, and whose product is square. Cycles in this graph have a parity, that is, they are either even (termed e-cycles) or odd (termed o-cycles). The absence of e-cycles in the graph is shown to imply that the matrix product is a P0-matrix, i.e., all of its principal minors are nonnegative. Conversely, the presence of an e-cycle is shown to imply that there exists a list of matrices associated with the graph whose product fails to be a P0-matrix. The results generalise a number of previous results relating P- and P0-matrices to graphs.
Keywords
Cite
@article{arxiv.1006.0152,
title = {P-matrices and signed digraphs},
author = {Murad Banaji and Carrie Rutherford},
journal= {arXiv preprint arXiv:1006.0152},
year = {2010}
}