Majorization for (0,±1)-matrices

Geir Dahl; Alexander Guterman; Pavel Shteyner

doi:10.1016/j.laa.2023.01.009

Majorization for (0,±1)-matrices

Geir Dahl, Alexander Guterman, Pavel Shteyner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1016/j.laa.2023.01.009
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

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10.1016/j.laa.2023.01.009

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AU - Shteyner, Pavel

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AB - 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.

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ER -

Majorization for (0,±1)-matrices

Abstract

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Funding

Keywords

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