An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices

Abstract

A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randić matrix of a connected graph.

arXiv comment11 pages, 2 figures, final version will appear in Linear Algebra and its Application