On linear preservers of sgut-majorization on $\textbf{M}_{n,m}$

Document Type: Research Paper

Author

Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.

Abstract

‎Let $\textbf{M}_{n,m}$ be the set of $n$-by-$m$‎ ‎matrices with entries in the field of real numbers‎. ‎A matrix $R$ in $\textbf{M}_{n}=\textbf{M}_{n,n}$ is a generalized row substochastic matrix (g-row substochastic‎, ‎for short) if $Re\leq e$‎, ‎where $e=(1,1,\ldots,1)^t$‎. ‎For $X,$ $Y \in \textbf{M}_{n,m}$‎, ‎$X$ is said to be sgut-majorized by $Y$ (denoted by $X‎ ‎\prec_{sgut} Y$) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $X=RY$‎. ‎This paper characterizes all‎ ‎linear preservers and strong linear preservers of $\prec_{sgut}$ on $\mathbb{R}^{n}$ and $\textbf{M}_{n,m}$ respectively‎.

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