TY - JOUR ID - 3147 TI - Strictly sub row Hadamard majorization JO - Journal of Mahani Mathematical Research JA - JMMR LA - en SN - 2251-7952 AU - Askarizadeh, Abbas AD - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Y1 - 2022 PY - 2022 VL - 11 IS - 1 SP - 159 EP - 168 KW - Linear preserver‎ KW - ‎Strong linear preserver‎ KW - ‎Strictly sub row stochastic‎ matrices DO - 10.22103/jmmrc.2021.18576.1177 N2 - ‎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. UR - https://jmmrc.uk.ac.ir/article_3147.html L1 - https://jmmrc.uk.ac.ir/article_3147_7669b32a3aa572846155f8686997c8a2.pdf ER -