## Abstract

Matrix majorization is a generalization of the classical majorization for vectors. We study several basic questions concerning matrix majorization for (0,±1)-matrices, i.e., matrices whose entries are restricted to 0, 1 and −1. In particular, we characterize when the zero vector is weakly majorized by a matrix, and show related results. Connections to linear programming are discussed. We obtain simpler characterizations of majorization under different assumptions. Also, several results on directional and strong majorization for (0,±1)-matrices are shown.

Original language | English |
---|---|

Pages (from-to) | 200-221 |

Number of pages | 22 |

Journal | Linear Algebra and Its Applications |

Volume | 663 |

DOIs | |

State | Published - 15 Apr 2023 |

### Bibliographical note

Publisher Copyright:© 2023 The Author(s)

### Funding

The authors are grateful to the referee for the useful comments. The work of the third author is financially supported by the Russian Science Foundation under the grant 21-11-00283 .

Funders | Funder number |
---|---|

Russian Science Foundation | 21-11-00283 |

## Keywords

- (0,±1)-matrices
- Linear programming
- Matrix majorization