A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Abstract

A set in the complex plane which involves n parameters in [ , ] is given to localize all eigenvalues di erent from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we x n parameters in [ , ] to give a new set including all eigenvalues di erent from , which is tighter than those provided by Shen et al.