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.
Bibliographical noteFunding 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 .
© 2023 The Author(s)
- Linear programming
- Matrix majorization