Arithmetic, geometric, and harmonic means for accretive-dissipative matrices
Functional Analysis
2022-10-18 v4
Abstract
The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM inequality is established for two accretive-dissipative matrices in the sense of this extended Loewner order. We also compare the harmonic mean and parallel sum of two accretive-dissipative matrices, revealing an interesting relation between them. A number of examples are included.
Keywords
Cite
@article{arxiv.1206.0370,
title = {Arithmetic, geometric, and harmonic means for accretive-dissipative matrices},
author = {Minghua Lin},
journal= {arXiv preprint arXiv:1206.0370},
year = {2022}
}
Comments
This preprint is of very little scientific value