An algorithm for constructing integral row stochastic matrices

Ilkhanizadeh Manesh, Asma

doi:10.22103/jmmrc.2021.13883.1089

An algorithm for constructing integral row stochastic matrices

Document Type : Research Paper

Author

Asma Ilkhanizadeh Manesh

Department of Mathematics Vali-e-Asr University of Rafsanjan P.O. Box: 7713936417, Rafsanjan, Iran

10.22103/jmmrc.2021.13883.1089

Abstract

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.

Keywords

Eigenvalue

Majorization

Integral row stochastic

20.1001.1.22517952.2022.11.1.5.1

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