## Intervals of special sign regular matrices

- We consider classes of n-by-n sign regular matrices, i.e., of matrices with the property that all their minors of fixed order k have one specified sign or are allowed also to vanish, k = 1, ... ,n. If the sign is nonpositive for all k, such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard partial ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the n-by-n matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.

Author: | Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND |
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DOI: | https://doi.org/10.1080/03081087.2015.1090388 |

ISSN: | 0308-1087 |

Parent Title (German): | Linear and Multilinear Algebra |

Volume: | 64 |

Document Type: | Article |

Language: | German |

Year of Publication: | 2016 |

Release Date: | 2019/05/16 |

Tag: | Sign regular matrix; Totally nonnegative matrix; Totally nonpositve matrix; Cauchon algorithm; Checkerboard ordering |

Issue: | 7 |

First Page: | 1424 |

Last Page: | 1444 |

Relevance: | Peer reviewed Publikation in Master Journal List |

Open Access?: | Nein |