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.
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