Advances in Operator Theory

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

Ahmad Mohammadhasani and Asma Ilkhanizadeh Manesh

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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

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

Received: 6 September 2017
Accepted: 3 December 2017
First available in Project Euclid: 21 December 2017

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Digital Object Identifier

Primary: 15A04: Linear transformations, semilinear transformations
Secondary: 15A51

linear preserver right matrix majorization row stochastic matrix


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.

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