既约随机矩阵的一些性质

Some Properties of Irreducible Stochastic Matrix

中文关键词:  既约矩阵  随机矩阵  双随机矩阵

英文关键词:irreducible matrix  stochastic matrix  doubly stochastic matrix.

中文摘要:

      本文讨论了既约广义随机矩阵特征值的性质，得到了双随机矩阵的益为既约矩阵的充要条件，以及P类矩阵的一些性质．

英文摘要:

      In this paper we obtained the following main results:Theorem 1 If A= (a_ij)_n×n is irreducible generalized stochastic matrix for which the sum ofevery equals s, and a_jj≠0, j=1,…,n, then λ=s is unique eigenvalue of A, whose module equals s.Theorem 2 If A= (a_ij)_n×n∈P,B=(b_ij)_n×n∈P, then AB∈P.Theorem 3 Suppose A= (a_ij)_n×n is doubly stochastic matrix, and a_jj≠0, j=1,…,n, then A^m is irreducible matrix, if and only if A is irreducible matrix, where m is an arbitrary natural number.