Strictly sub row Hadamard majorization
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 Hada...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2022-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3147_7669b32a3aa572846155f8686997c8a2.pdf |
| Summary: | 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. |
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| ISSN: | 2251-7952 2645-4505 |