# 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.

Authors | Banaji, M and Rutherford, CG |
---|---|

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. |

Year | 2010 |

Journal | Discrete Mathematics |

Journal citation | 311 (4), pp. 295-301 |

Publisher | London South Bank University |

ISSN | 0012-365X |

Digital Object Identifier (DOI) | doi:10.1016/j.disc.2010.10.018 |

Publication dates | |

Print | 18 Nov 2010 |

Publication process dates | |

Deposited | 19 Dec 2017 |

Accepted | 22 Oct 2010 |

Accepted author manuscript | License CC BY-NC-ND 4.0 |

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https://openresearch.lsbu.ac.uk/item/87q02

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