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Summer 2018 Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$
Ahmad Mohammadhasani, Asma Ilkhanizadeh Manesh
Adv. Oper. Theory 3(3): 451-458 (Summer 2018). DOI: 10.15352/aot.1709-1225

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].

Citation

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Ahmad Mohammadhasani. Asma Ilkhanizadeh Manesh. "Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$." Adv. Oper. Theory 3 (3) 451 - 458, Summer 2018. https://doi.org/10.15352/aot.1709-1225

Information

Received: 6 September 2017; Accepted: 3 December 2017; Published: Summer 2018
First available in Project Euclid: 21 December 2017

zbMATH: 1392.15041
MathSciNet: MR3795093
Digital Object Identifier: 10.15352/aot.1709-1225

Subjects:
Primary: 15A04
Secondary: 15A51

Keywords: linear preserver , right matrix majorization , row stochastic matrix

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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