Abstract :
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 $A,Bintextbf{M}_{m,n}$, we say that $A$ is strictly sub row Hadamard majorized by $B$ (denoted by $Aprec_{SH}B)$ if there exists an $m$by$n$ strictly sub row stochastic matrix $R$ such that $A=Rcirc B$ where $X circ Y$ is the Hadamard product (entrywise product) of matrices $X,Yintextbf{M}_{m,n}$. 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.
Keywords :
Linear preserver , Strong linear preserver , Strictly sub row Hadamard majorization , Strictly sub row stochastic
