An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices
type: Item
instance of: scholarly article
title: An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices
zbMATH Open document ID: 1260.15035
author: Takeaki Yamazaki
published in: Linear Algebra and its Applications
publication date: 2013-03-06T00:00:00Z
review text: The definition of the weighted Riemannian mean (WRM) and its known equational characterization are introduced in this article. This mean satisfies the famous ten properties of the ALM mean referring to Ando, Li, and Mathias. The author obtains a simple proof for arithmetic-geometric-harmonic mean inequalities of the WRM.
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 6142075
zbMATH Keywords: positive definite matrix
zbMATH Keywords: geometric mean
zbMATH Keywords: the Riemannian mean
zbMATH Keywords: matrix inequality
zbMATH Keywords: arithmetic-geometric mean inequality
Wikidata QID: Q115344728
reviewed by: Fozi Dannan
MaRDI profile type: Publication
full work available at URL: j.laa.2011.12.006
OpenAlex ID: W2002768246
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DOI: 10.1016/J.LAA.2011.12.006
description: scientific article; zbMATH DE number 6142075