%0 Journal Article %T Strictly sub row Hadamard majorization %J Journal of Mahani Mathematical Research %I Shahid Bahonar University of Kerman %Z 2251-7952 %A Askarizadeh, Abbas %D 2022 %\ 01/01/2022 %V 11 %N 1 %P 159-168 %! Strictly sub row Hadamard majorization %K Linear preserver‎ %K ‎Strong linear preserver‎ %K ‎Strictly sub row stochastic‎ matrices %R 10.22103/jmmrc.2021.18576.1177 %X ‎Let $\textbf{M}_{m,n}$ be the set of all $m$-by-$n$ real matrices‎. ‎A matrix $R$ in $\textbf{M}_{m,n}$ with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of $R$ is less than 1‎. ‎For $A,B\in\textbf{M}_{m,n}$‎, ‎we say that $A$ is strictly sub row Hadamard majorized by $B$ (denoted by $A\prec_{SH}B)$ if there exists an $m$-by-$n$ strictly sub row stochastic matrix $R$ such that $A=R\circ B$ where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X,Y\in\textbf{M}_{m,n}$‎. ‎In this paper‎, ‎we introduce the concept of strictly sub row Hadamard majorization as a relation on $\textbf{M}_{m,n}$‎. ‎Also‎, ‎we find the structure of all linear operators $T:\textbf{M}_{m,n} \rightarrow \textbf{M}_{m,n}$ which are preservers (resp‎. ‎strong preservers) of strictly sub row Hadamard majorization‎. %U https://jmmrc.uk.ac.ir/article_3147_7669b32a3aa572846155f8686997c8a2.pdf