Row Stochastic Matrices and Linear Preservers of Matrix Majorization $T:\mathbb{R}_{m} \rightarrow \mathbb{R}_{n}$

Document Type : Original Scientific Paper

Authors

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

Abstract

‎A nonnegative square and real matrix $R$ is a row stochastic matrix if the sum of the entries of each row is equal to one‎. ‎Let $x$‎, ‎$y \in \mathbb{R}_{n}$‎. ‎The vector $x$ is said to be matrix majorized by $y$ and denoted by $ x\prec_{r} y$ if $x=yR$ for some row stochastic matrix $R$‎. ‎In the present paper‎, ‎we characterize the linear preservers of matrix majorization $T:\mathbb{R}_{m} \rightarrow \mathbb{R}_{n}$‎.

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References

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Mathematics Interdisciplinary Research
Volume 8, Issue 4
December 2023
Pages 291-307

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