An algorithm for constructing integral row stochastic matrices

Document Type : Research Paper

Author

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

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

References

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History

  • Receive Date: 21 April 2019
  • Revise Date: 21 November 2021
  • Accept Date: 03 December 2021

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