An eigenvalue localization theorem for stochastic matrices and its application to Randi\'c matrices

摘要

A square matrix is called stochastic (or row-stochastic) if it isnon-negative and has each row sum equal to unity. Here, we constitute aneigenvalue localization theorem for a stochastic matrix, by using its principalsubmatrices. As an application, we provide a suitable bound for theeigenvalues, other than unity, of the Randi\'c matrix of a connected graph.