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An algorithm for constructing integral row stochastic matrices | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 1 - شماره پیاپی 21، فروردین 2022، صفحه 69-77 اصل مقاله (481.83 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.13883.1089 | ||
| نویسنده | ||
| Asma Ilkhanizadeh Manesh* | ||
| Department of Mathematics Vali-e-Asr University of Rafsanjan P.O. Box: 7713936417, Rafsanjan, Iran | ||
| چکیده | ||
| Let $\textbf{M}_{n}$ be the set of all $n$-by-$n$ real matrices, and let $\mathbb{R}^{n}$ be the set of all $n$-by-$1$ real (column) vectors. An $n$-by-$n$ matrix $R=[r_{ij}]$ with nonnegative entries is called row stochastic, if $\sum_{k=1}^{n} r_{ik}$ is equal to 1 for all $i$, $(1\leq i \leq n)$. In fact, $Re=e$, where $e=(1,\ldots,1)^t\in \mathbb{R}^n$. A matrix $R\in \textbf{M}_{n}$ is called integral row stochastic, if each row has exactly one nonzero entry, $+1$, and other entries are zero. In the present paper, we provide an algorithm for constructing integral row stochastic matrices, and also we show the relationship between this algorithm and majorization theory. | ||
| کلیدواژه‌ها | ||
| Eigenvalue؛ Majorization؛ Integral row stochastic | ||
| مراجع | ||
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[6] A. Ilkhanizadeh Manesh, Sglt-Majorization on Mn;m and its linear preservers, J. Mahani Mathematical Reserch Center, 7, (2018), 57-125.
[7] A. Ilkhanizadeh Manesh, Right gut-Majorization on Mn;m, Electron. J. Linear Algebra, 31, (2016), 13-26.
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