Linear preservers of Miranda-Thompson majorization on MM;N

Document Type : Research Paper


1 Department of Mathematics, Sirjan University of technology, Sirjan, Iran

2 Vali-e-Asr University of Rafsanjan



Miranda-Thompson majorization is a group-induced cone ordering on $\mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Y\in M_{m,n}$, $X$ is said to be  Miranda-Thompson majorized by $Y$ (denoted by $X\prec_{mt}Y$) if there exists some $D\in \rm{Conv(G)}$ such that $X=DY$.  Also, we characterize linear preservers of this concept on $M_{m,n}$.


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