Two-sided sgut-majorization and its linear preservers
Let $\textbf{M}_{n,m}$ be the set of all $n$-by-$m$ real matrices, and let $\mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. An $n$-by-$m$ matrix $R=[r_{ij}]$ is called g-row substochastic if $\sum_{k=1}^{m} r_{ik}\leq 1$ for all $i\ (1\leq i \leq n)$. For $x$, $y \in \mathbb{R}^{n}...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2023-05-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3508_4f357c6d810b494a09db0de54e0202d2.pdf |
| Summary: | Let $\textbf{M}_{n,m}$ be the set of all $n$-by-$m$ real matrices, and let $\mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. An $n$-by-$m$ matrix $R=[r_{ij}]$ is called g-row substochastic if $\sum_{k=1}^{m} r_{ik}\leq 1$ for all $i\ (1\leq i \leq n)$. For $x$, $y \in \mathbb{R}^{n}$, it is said that $x$ is $\textit{sgut-majorized}$ by $y$, and we write $ x \prec_{sgut}y$ if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=Ry$. Define the relation $\sim_{sgut}$ as follows. $x\sim_{sgut}y$ if and only if $x$ is sgut-majorized by $y$ and $y$ is sgut-majorized by $x$. This paper characterizes all (strong) linear preservers of $\sim_{sgut}$ on $\mathbb{R}^{n}$. |
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| ISSN: | 2251-7952 2645-4505 |