Please use this identifier to cite or link to this item:

`https://hdl.handle.net/1822/2873`

Title: | The symmetric N-matrix completion problem |

Author(s): | Araújo, C. Mendes Torregrosa, Juan R. Urbano, Ana M. |

Keywords: | Partial matrix Matrix completion problems N-matrix Undirected graphs completion problem undirected graph |

Issue date: | 1-Sep-2005 |

Publisher: | Elsevier |

Journal: | Linear Algebra and its Applications |

Citation: | Araújo, C. M., Torregrosa, J. R., & Urbano, A. M. (2005, September). The symmetric N-matrix completion problem. Linear Algebra and its Applications. Elsevier BV. http://doi.org/10.1016/j.laa.2005.04.008 |

Abstract(s): | An $n\times n$ matrix is called an $N$-matrix if all its principal minors are negative. In this paper, we are interested in the symmetric $N$-matrix completion problem, that is, when a partial symmetric $N$-matrix has a symmetric $N$-matrix completion. Here, we prove that a partial symmetric $N$-matrix has a symmetric $N$-matrix completion if the graph of its specified entries is chordal. Furthermore, if this graph is not chordal, then examples exist without symmetric $N$-matrix completions. Necessary and sufficient conditions for the existence of a symmetric $N$-matrix completion of a partial symmetric $N$-matrix whose associated graph is a cycle are given. |

Type: | Article |

URI: | https://hdl.handle.net/1822/2873 |

DOI: | 10.1016/j.laa.2005.04.008 |

ISSN: | 0024-3795 |

Publisher version: | https://www.sciencedirect.com/science/article/pii/S0024379505002338 |

Peer-Reviewed: | yes |

Access: | Open access |

Appears in Collections: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |

Files in This Item:

File | Description | Size | Format | |
---|---|---|---|---|

symNmat.pdf | Documento principal | 136,84 kB | Adobe PDF | View/Open |