Original version
Linear Algebra and its Applications. 2023, DOI: https://doi.org/10.1016/j.laa.2023.01.009
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.