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

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 $T:\mathbb{R}_{m} \rightarrow \mathbb{R}_{n}$‎.

Keywords

• linear preserver‎
• ‎matrix majorization‎
• ‎$m$-{r}ow stochastic matrix