en تخصصي Special پژوهشي Research paper <p>Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if there exists an $n$-by-$n$ upper triangular row substochastic matrix $R$ such that $x=Ry$. In this note, we characterize the linear functions $T$ : $mathbb{R}^n$ $rightarrow$ $mathbb{R}^n$ preserving (resp. strongly preserving) $prec_{sut}$ with additional condition $Te_{1}neq 0$ (resp. no additional conditions).</p> (Strong) linear preserver, Row substochastic matrix, Sut-Majorization. 111 118 http://ijmsi.ir/browse.php?a_code=A-10-690-1&slc_lang=en&sid=1 A. Ilkhanizadeh Manesh a.ilkhani@vru.ac.ir 10031947532846003963 10031947532846003963 Yes Department of Mathematics,Vali-e-Asr University of Rafsanjan