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

Funding Information:
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 .

Publisher Copyright:
© 2023 The Author(s)

Keywords

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

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10.1016/j.laa.2023.01.009

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AU - Guterman, Alexander

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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Keywords

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