## Advances in Operator Theory

- Adv. Oper. Theory
- Volume 3, Number 3 (2018), 451-458.

### Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$

Ahmad Mohammadhasani and Asma Ilkhanizadeh Manesh

#### Abstract

A nonnegative real matrix $R \in \mathrm {M}_{n,m}$ with the property that all its row sums are one is said to be row stochastic. For $x, y \in \mathbb{R}_{n}$, we say $x$ is right matrix majorized by $y$ (denoted by $x \prec_{r} y$) if there exists an $n$-by-$n$ row stochastic matrix $R$ such that $x = yR$. The relation $\sim_{r}$ on $\mathbb{R}_{n}$ is defined as follows. $x \sim_{r}y$ if and only if $x \prec_{r} y \prec_{r} x$. In the present paper, we characterize the linear preservers of $\sim_{r}$ on $\mathbb{R}_{n}$, and answer the question raised by F. Khalooei [Wavelet Linear Algebra **1** (2014), no. 1, 43-50].

#### Article information

**Source**

Adv. Oper. Theory, Volume 3, Number 3 (2018), 451-458.

**Dates**

Received: 6 September 2017

Accepted: 3 December 2017

First available in Project Euclid: 21 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aot/1513876632

**Digital Object Identifier**

doi:10.15352/aot.1709-1225

**Mathematical Reviews number (MathSciNet)**

MR3795093

**Zentralblatt MATH identifier**

1392.15041

**Subjects**

Primary: 15A04: Linear transformations, semilinear transformations

Secondary: 15A51

**Keywords**

linear preserver right matrix majorization row stochastic matrix

#### Citation

Mohammadhasani, Ahmad; Ilkhanizadeh Manesh, Asma. Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$. Adv. Oper. Theory 3 (2018), no. 3, 451--458. doi:10.15352/aot.1709-1225. https://projecteuclid.org/euclid.aot/1513876632