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 $i$, $(1leq i leq n)$. In fact, $Re=e$, where $e=(1,ldots,1)^tin mathbb{R}^n$. A matrix $Rin textbf{M}_{n}$ 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.
