Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(6): 1691-1701

Online first article April 9, 2018      Printed November 30, 2018

https://doi.org/10.4134/BKMS.b170964

Copyright © The Korean Mathematical Society.

On the location of eigenvalues of real constant row-sum matrices

Frank J. Hall, Rachid Marsli

Georgia State University, King Fahd University of Petroleum and Minerals

Abstract

New inclusion sets are obtained for the eigenvalues of real matrices for which the all $1$'s vector is an eigenvector, i.e., the constant row-sum real matrices. A number of examples are provided. This paper builds upon the work of the authors in \cite{HM3}. The results of this paper are in terms of Ger\v{s}gorin discs of the second type. An application of the main theorem to bounding the algebraic connectivity of connected simple graphs is obtained.

Keywords: e-matrix, stochastic matrix, eigenvalue, Gersgorin disc, radius

MSC numbers: 15A18, 15A42, 15B51