On the location of eigenvalues of real constant row-sum matrices
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1691-1701
Published online April 9, 2018
Printed November 30, 2018
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
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