# Numerical radius inequalities of operator matrices with applications

## TL;DR

This paper develops improved bounds for the numerical radius of 2x2 operator matrices and applies these results to obtain better estimates for polynomial zeros.

## Contribution

It introduces tighter bounds for the numerical radius of operator matrices and demonstrates their application in polynomial zero estimation.

## Key findings

- Improved bounds for the numerical radius of 2x2 operator matrices.
- Enhanced estimation of polynomial zeros using the new bounds.
- Better understanding of operator matrix behavior in numerical radius context.

## Abstract

We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the results obtained we give a better estimation for the zeros of a polynomial.