Singular Values Inequalities for Matrix Means

TL;DR

This paper establishes new inequalities involving the singular values of differences of matrix means, refining existing results and providing additional matrix mean inequalities.

Contribution

It introduces novel inequalities for singular values of matrix mean differences, enhancing the theoretical understanding of matrix inequalities.

Findings

Refined inequalities for singular values of matrix mean differences

Additional matrix mean inequalities derived

Complemented well-established results in literature

Abstract

In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values inequalities, we will show several matrix means inequalities, as well.