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