Inequalities for arithmetic–geometric–harmonic means of sector matrices

Abstract

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.

Keywords:

• Inequality
• geometric mean
• arithmetic mean
• harmonic mean
• sector matrix

2010 Mathematics Subject Classifications:

• 15A45
• 15A60

Acknowledgments

The authors are grateful to the referee for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported in part by the National Natural Science Foundation of China [grant numbers 11871249, 11871326, 11931009].