%0 Journal Article
%T Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Mohammadhasani, Ahmad
%A Ilkhanizadeh Manesh, Asma
%D 2018
%\ 07/01/2018
%V 3
%N 3
%P 451-458
%! Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$
%K Linear preserver
%K right matrix majorization
%K row stochastic matrix
%R 10.15352/aot.1709-1225
%X A nonnegative real matrix $Rin textbf{M}_{n,m}$ 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 $xprec_{r} y$) 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. $xsim_{r}y$ if and only if $ xprec_{r} yprec_{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 textbf{1} (2014), no. 1, 43--50].
%U http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf