Generalization of some results concerning eigenvalues of a certain class of matrices and some applications

TL;DR

This paper generalizes spectral properties of a class of block matrices and explores implications for nonnegative matrices, doubly stochastic matrices, and graph theory, including graph spectra and energy.

Contribution

It introduces a broad generalization of existing eigenvalue results for block matrices and applies these findings to various matrix classes and graph theoretical concepts.

Findings

Extended eigenvalue results for a class of block matrices.

Implications for nonnegative and doubly stochastic matrices.

Applications to graph spectra and graph energy.

Abstract

In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and graph theory namely on graph spectra and graph energy.