On some inequalities for the matrix power and Karcher means
type: Item
instance of: scholarly article
title: On some inequalities for the matrix power and Karcher means
zbMATH Open document ID: 1260.15032
author: Yongdo Lim
author: Takeaki Yamazaki
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: The authors have establish a useful inequality for matrix power means of positive definite matrices. The paper provides 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.
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 6125865
zbMATH Keywords: positive definite matrix
zbMATH Keywords: power mean
zbMATH Keywords: Karcher mean
zbMATH Keywords: matrix mean inequalities
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
full work available at URL: j.laa.2012.08.023
OpenAlex ID: W2089884622
cites work: Log majorization and complementary Golden-Thompson type inequalities
cites work: The resolvent average for positive semidefinite matrices
cites work: Q5690490
cites work: On the exponential metric increasing property.
cites work: Q3425149
cites work: The Riemannian Mean of Positive Matrices
cites work: Riemannian geometry and matrix geometric means
cites work: Monotonicity of the matrix geometric mean
cites work: Q4419562
cites work: No dice: a deterministic approach to the Cartan centroid
cites work: The matrix geometric mean of parameterized, weighted arithmetic and harmonic means
cites work: Q4226699
cites work: The Geometric Mean, Matrices, Metrics, and More
cites work: Monotonic properties of the least squares mean
cites work: Karcher means and Karcher equations of positive definite operators
cites work: Matrix power means and the Karcher mean
cites work: A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
cites work: The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
DOI: 10.1016/J.LAA.2012.08.023
description: scientific article; zbMATH DE number 6125865