On a reverse of the Tan-Xie inequality for sector matrices and its applications

TL;DR

This paper proves a reverse inequality for sector matrices building on Tan and Xie's work, and applies it to derive new inequalities related to determinants and unitarily invariant norms.

Contribution

It introduces a reverse of the Tan-Xie inequality for sector matrices using the Kantorovich constant, with applications to determinants and norms.

Findings

Established a reverse inequality for sector matrices.

Derived new inequalities for determinants.

Presented inequalities involving unitarily invariant norms.

Abstract

In this short paper, we establish a reverse of the derived inequalities for sector matrices by Tan and Xie, with Kantorovich constant. Then, as application of our main theorem, some inequalities for determinant and unitarily invariant norm are presented.