P-matrices and signed digraphs

Journal article

Banaji, M and Rutherford, CG (2010). P-matrices and signed digraphs. Discrete Mathematics. 311 (4), pp. 295-301. https://doi.org/10.1016/j.disc.2010.10.018
AuthorsBanaji, M and Rutherford, CG

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.

JournalDiscrete Mathematics
Journal citation311 (4), pp. 295-301
Digital Object Identifier (DOI)https://doi.org/10.1016/j.disc.2010.10.018
Publication dates
Print18 Nov 2010
Publication process dates
Deposited19 Dec 2017
Accepted22 Oct 2010
Accepted author manuscript
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