%0 Journal Article
%T Row stochastic inverse eigenvalue problem
%A Shang-jun Yang
%A Chang-qing Xu
%J Journal of Inequalities and Applications
%D 2011
%I Springer
%X In this paper, we give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum ¦« = {¦Ë1, ..., ¦Ën} = ¦«1 ¡È   ¡È ¦«m ¡È ¦«m+1, m > 0; where (pk is an integer greater than 1), ¦Ëk1 = ¦Ëk > 0, 1 = ¦Ë1 ¡Ý ¦Øk > 0, k = 1, ..., m; ¦«m+1 = {¦Ëm+1}, ¦Øm+1 ¡Ô ¦Ë1 + ..., +¦Ën ¡Ü ¦Ë1, ¦Øk ¡Ý ¦Ëk, ¦Ø1 ¡Ý ¦Ëk, k = 2, ..., m + 1. In the case when p1, ..., pm are all equal to 2, ¦« 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.
%K row stochastic matrices
%K inverse eigenvalue problem
%K row stochastic inverse eigenvalue problem
%U http://www.journalofinequalitiesandapplications.com/content/2011/1/24