An algorithm for constructing integral row stochastic matrices

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-۱ real (column) vectors. An n-by-n matrix R=[r_{ij}] with nonnegative entries is called row stochastic, if \sum_{k=۱}^{n} r_{ik} is equal to ۱ for all i, (۱\leq i \leq n). In fact, Re=e, where e=(۱,\ldots,۱)^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, +۱, 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