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

Xiaoxiao Wang, Chaoqian Li, Yaotang Li
2018 Open Mathematics  
A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different 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 fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and
more » ... inear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.
doi:10.1515/math-2018-0030 fatcat:ac4rjknwn5ewvpesqxux6nsxom