Numerical radii of accretive matrices

TL;DR

This paper introduces new bounds for the numerical radius of accretive matrices, offering refined inequalities and novel insights specific to this class of matrices, which are important in matrix analysis.

Contribution

It presents a new approach to bounding the numerical radius of accretive matrices, including several refined and novel inequalities specific to this class.

Findings

New bounds for the numerical radius of accretive matrices

Refinements of existing inequalities for positive matrices

Introduction of a novel approach for accretive matrices

Abstract

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in the literature. In this article, we present many new bounds for the numerical radius of accretive matrices. The importance of this study is the presence of a new approach that treats a specific class of matrices, namely the accretive ones. The new bounds provide a new set of inequalities, some of which can be considered as refinements of other existing ones, while others present new insight to some known results for positive matrices.