Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$4514585365410.15352/aot.1709-1225ENAhmad MohammadhasaniAsma Ilkhanizadeh ManeshRafsanjan University of Vali AsrJournal Article20170906A 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].http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf