Triangle inequalities for the operator symmetric modulus

TL;DR

This paper investigates the properties of the operator symmetric modulus for matrices, establishing several triangle inequalities to deepen understanding of its mathematical behavior.

Contribution

It introduces new triangle inequalities related to the operator symmetric modulus, expanding theoretical knowledge in matrix analysis.

Findings

Derived multiple triangle inequalities for the operator symmetric modulus.

Enhanced understanding of the mathematical properties of matrix moduli.

Provided theoretical foundations for further research in operator theory.

Abstract

We study the operator symmetric modulus (|Z|+|Z^*|)/2 for matrices Z. Several triangle type inequalities are given.