Norm inequalities related to the matrix geometric mean

TL;DR

This paper explores inequalities involving the norms of various forms of the matrix geometric mean for positive definite matrices, providing insights into their relationships and bounds.

Contribution

It introduces new inequalities relating different versions of the matrix geometric mean and their norms, advancing understanding in matrix analysis.

Findings

Established bounds for matrix geometric mean norms

Compared different geometric mean variants

Provided theoretical inequalities for positive definite matrices

Abstract

Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.