Generalizations of Enestrom-Kakeya Type Theorems for matrix Polynomials

TL;DR

This paper extends classical eigenvalue bounds to matrix polynomials, providing new generalizations of the Enestrom-Kakeya Theorem to better understand their spectral properties.

Contribution

It introduces novel bounds for eigenvalues of matrix polynomials, generalizing the Enestrom-Kakeya Theorem beyond scalar cases.

Findings

Derived new eigenvalue bounds for matrix polynomials

Generalized classical scalar theorems to matrix settings

Enhanced understanding of spectral bounds for matrix polynomials

Abstract

In this paper, we establish bounds for the eigenvalues of matrix polynomials. Specifically, we find different generalizations of the Enestrom-Kakeya Theorem for matrix polynomials.