Generalization of Cauchy type theorems for matrix Polynomials

TL;DR

This paper extends classical Cauchy theorems to matrix polynomials, providing bounds for their eigenvalues and generalizing the distribution of eigenvalues.

Contribution

It introduces generalized bounds for eigenvalues of matrix polynomials, extending classical scalar results to matrix cases.

Findings

Derived new bounds for eigenvalues of matrix polynomials

Generalized Cauchy's theorem for matrix eigenvalue distribution

Extended classical scalar results to matrix polynomial context

Abstract

In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.