English

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

Combinatorics 2016-05-02 v2

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 Randi\'c matrix of a connected graph.

Keywords

Cite

@article{arxiv.1601.07736,
  title  = {An eigenvalue localization theorem for stochastic matrices and its application to Randi\'c matrices},
  author = {Anirban Banerjee and Ranjit Mehatari},
  journal= {arXiv preprint arXiv:1601.07736},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-22T12:38:32.402Z