Row stochastic inverse eigenvalue problem

In this paper, we give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum Λ = {λ1, ..., λn} = Λ1 ∪ ∪ Λm ∪ Λm+1, m > 0; where (pk is an integer greater than 1), λk1 = λk > 0, 1 = λ1 ≥ ωk > 0, k = 1, ..., m; Λm+1 = {λm+1}, ωm+1 ≡ λ1 + ..., +λn ≤ λ1, ωk ≥ λk, ω1 ≥ λk, k = 2, ..., m + 1. In the case when p1, ..., pm are all equal to 2, Λ becomes a list of 2m + 1 real numbers for any positive integer m, and our result gives sufficient conditions for a list of 2m + 1 real numbers to be realizable by a row stochastic matrix. AMS classification: 15A18.