Majorization for (0,±1)-matrices

Geir Dahl, Alexander Guterman, Pavel Shteyner

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)200-221
Number of pages22
JournalLinear Algebra and Its Applications
StatePublished - 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)


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


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