Row stochastic inverse eigenvalue problem
Yang Shang-jun, Changqing Xu · Journal of Inequalities and Applications · 2011
In this paper, we give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum Λ = {λ1, ..., λ n } = Λ1 ∪ ⋯ ∪ Λ m ∪ Λm+1, m > 0; where (p k is an integer greater than 1), λk 1= λ k > 0, 1 = λ1 ≥ ω k > 0, k = 1, ..., m; Λm+1= {λ m +1}, ωm+1≡ λ1 + ..., +λ n ≤ λ1, ω k ≥ λ k , ω1 ≥ λ k , k = 2, ..., m + 1. In the case when p1, ..., p m 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.