On some inequalities for the matrix power and Karcher means

Yongdo Lim; Takeaki Yamazaki

doi:10.1016/j.laa.2012.08.023

On some inequalities for the matrix power and Karcher means

Yongdo Lim
, Takeaki Yamazaki

Department of Mathematics

Toyo University

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We establish a useful inequality for matrix power means of positive definite matrices. It eventually provides not only a new characterization of the Karcher mean (Cartan centroid, Riemannian geometric mean) but also a simple proof of the convergence of power means to the Karcher mean. Some new matrix mean inequalities on the Karcher and power means are presented.

Original language	English
Pages (from-to)	1293-1304
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	3
DOIs	https://doi.org/10.1016/j.laa.2012.08.023
State	Published - 1 Feb 2013

Keywords

Inequality
Karcher mean
Positive definite matrix
Power mean

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10.1016/j.laa.2012.08.023

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title = "On some inequalities for the matrix power and Karcher means",

abstract = "We establish a useful inequality for matrix power means of positive definite matrices. It eventually provides not only a new characterization of the Karcher mean (Cartan centroid, Riemannian geometric mean) but also a simple proof of the convergence of power means to the Karcher mean. Some new matrix mean inequalities on the Karcher and power means are presented.",

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AU - Lim, Yongdo

AU - Yamazaki, Takeaki

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N2 - We establish a useful inequality for matrix power means of positive definite matrices. It eventually provides not only a new characterization of the Karcher mean (Cartan centroid, Riemannian geometric mean) but also a simple proof of the convergence of power means to the Karcher mean. Some new matrix mean inequalities on the Karcher and power means are presented.

AB - We establish a useful inequality for matrix power means of positive definite matrices. It eventually provides not only a new characterization of the Karcher mean (Cartan centroid, Riemannian geometric mean) but also a simple proof of the convergence of power means to the Karcher mean. Some new matrix mean inequalities on the Karcher and power means are presented.

KW - Inequality

KW - Karcher mean

KW - Positive definite matrix

KW - Power mean

UR - https://www.scopus.com/pages/publications/84870356274

U2 - 10.1016/j.laa.2012.08.023

DO - 10.1016/j.laa.2012.08.023

M3 - Article

AN - SCOPUS:84870356274

SN - 0024-3795

VL - 438

SP - 1293

EP - 1304

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 3

ER -

On some inequalities for the matrix power and Karcher means

Abstract

Keywords

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