# Note on regions containing eigenvalues of a matrix

## TL;DR

This paper introduces a new eigenvalue inclusion region for matrices by refining existing lphaeta-type regions, providing a tighter bound on where eigenvalues can be located.

## Contribution

It proposes a novel eigenvalue inclusion region that is contained within the previous lphaeta-type region, improving eigenvalue localization.

## Key findings

- The new region is strictly contained within the previous lphaeta-type region.
- The paper proves the new region's validity and containment.
- The approach refines eigenvalue localization methods.

## Abstract

By excluding some regions, in which each eigenvalue of a matrix is not contained, from the \alpha\beta-type eigenvalue inclusion region provided by Huang et al.(Electronic Journal of Linear Algebra, 15 (2006) 215-224), a new eigenvalue inclusion region is given. And it is proved that the new region is contained in the \alpha\beta-type eigenvalue inclusion region.