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 $M_{m,n}$.


[1] L.B. Beasley, S-G. Lee and Y-H Lee, A characterization of strong preservers of matrix majorization, Linear Algebra Appl., 367 (2003), 341-346,
[2] H. Chiang and C.K. Li, Generalized doubly stochastic matrices and linear preservers, Linear Multilinear Algebra, 53(1) (2005), 1-11.
[3] A. Giovagnoli and H.P. Wynn, G-majorization with applications to matrix orderings, Linear Algebra Appl., 67 (1985), 111-135.
[4] A.M. Hasani and M. Radjabalipour, On linear preservers of (right) matrix majorization, Linear Algebra Appl., 423 (2007),  255-261.
[5] A. Ilkhanizadeh Manesh, Right gut-Majorization on M_{n,m}, Electron. J. Linear Algebra, 31(1) (2016), 13-26.
[6] F. Khalooei, Linear preservers of two-sided matrix majorization, Wavel. Linear Algebra, 1 (2014), 43-50.
[7] M. Niezgoda, Cone orderings, group majorizations and similarly separable vectors, Linear Algebra Appl., 436 (2012), 579-594.
[8] A.W. Marshall, I. Olkin, and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Springer, New York, 2011.

[9] M. Soleymani and A. Armandnejad, Linear preservers of even majorization on M_{n,m}, Linear Multilinear Algebra, 62(11) (2014), 1437-1449.