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

2016/01/28 by Anirban Banerjee, Banerjee, Anirban, Ranjit Mehatari +1 · 1 citation
Computer Science · Engineering · Mathematics · #05C50 #15A42 #15B51 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems #math.CO #msc:05C50 #msc:15A42 #msc:15B51

paper · pdf · doi:10.48550/arxiv.1601.07736

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

openalex publication_date 2016/01/28 · arxiv created 2016/04/29 · arxiv updated 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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