Inequalities for arithmetic-geometric-harmonic means of sector matrices

We provide upper and lower bounds for the weighted arithmetic mean, geometric mean and harmonic mean of a set of sector matrices. It generalizes Sagae and Tanabe's result in [Linear Multilinear Algebra. 1994;37:279-282] to multiple sector matrices. As an application of the bounds, we present inequalities for singular values, determinants and unitarily invariant norms.

Automated summary

This paper provides upper and lower bounds for the weighted arithmetic mean, geometric mean, and harmonic mean of a set of sector matrices, extending previous results by Sagae and Tanabe. In application, the study presents inequalities for singular values, determinants, and unitarily invariant norms.