# A note on multivariate majorization

Document Type : Research Paper

Authors

Department of Mathematics, Sirjan University of Technology, Sirjan, Iran

Abstract

‎A matrix $A$ is said to be multivariate majorized by a matrix $B$‎, ‎written $A\prec B$‎, ‎if there exists a doubly stochastic matrix $D$ such that $A = BD$‎ . ‎In the present paper‎, ‎we obtain a totally ordered subset of $M_{nm}$ which contains a given matrix $A$‎. ‎Also‎, ‎we show that the totality of all extreme points of the collection of all the matrices which are multivariate‏‎ly‎ majorized by a matrix $A$ is the set of all matrices obtained by permuting the columns of $A$‎.

Keywords

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### History

• Receive Date: 10 February 2022
• Revise Date: 21 April 2022
• Accept Date: 23 April 2022
• First Publish Date: 23 April 2022