Linear Preservers of Right SGUT-Majorization on $\mathbb{R}_{n}$

Document Type : Original Article

Authors

Ahmad Mohammadhasani ¹

Asma Ilkhanizadeh Manesh ²

¹ Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.

² Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O.Box: 7713936417, Rafsanjan, Iran.

10.22034/kjm.2017.49229

Abstract

A matrix $R$ is called a $\textit{generalized row substochastic}$ (g-row substochastic) if the sum of entries on every row of $R$ is less than or equal to one. For $x$, $y \in \mathbb{R}_{n}$, it is said that $x$ is $\textit{rsgut-majorized}$ by $y$ (denoted by $ x \prec_{rsgut} y$ ) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=yR$. In the present paper, we characterize the linear preservers and strong linear preservers of rsgut-majorization on
$\mathbb{R}_{n}$.

Keywords

Linear preserver

g-row substochastic matrix

rsgut-majorization

strong linear preserver

Subjects

• 15 Linear and multilinear algebra; matrix theory

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