A matrix trace inequality and its application

TL;DR

This paper proves a conjecture on matrix trace inequalities for positive semidefinite matrices and applies it to derive a generalized Golden-Thompson inequality, advancing understanding in matrix analysis.

Contribution

It provides a complete proof of a conjecture on matrix trace inequalities and introduces a generalized Golden-Thompson inequality for positive semidefinite matrices.

Findings

Proved a conjecture on matrix trace inequalities.

Derived a generalized Golden-Thompson inequality.

Enhanced theoretical understanding of positive semidefinite matrices.

Abstract

In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson inequality for positive semidefinite matrices.