P-matrices and signed digraphs

Murad Banaji, C. Rutherford

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)295-301
Number of pages7
JournalDiscrete Mathematics
Issue number4
Publication statusPublished - 2011


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