On some matrix inequalities.
type: Item
instance of: scholarly article
title: On some matrix inequalities.
zbMATH Open document ID: 1052.15016
author: Xingzhi Zhan
published in: Linear Algebra and its Applications
publication date: 2003-12-03T00:00:00Z
review text: The paper reproves the arithmetic-geometric mean inequality of \textit{R. Bhatia} and \textit{F. Kittaneh} [SIAM J. Matrix Anal. Appl. 11, No. 2, 272--277 (1990; Zbl 0704.47014)] in two equivalent versions via Weyl's monotonicity principle and a cleverly designed block matrix representaion for the inequality. The arithmetic-geometric mean inequality is then applied to quickly prove a generalization of the trace inequality of \textit{T. W. Anderson} and \textit{J. B. Taylor} [Linear Algebra Appl. 30, 93--99 (1980; Zbl 0434.15017)] to matrices, as well as a generalization to two matrices of the norm inequality of \textit{F. Kittaneh} [J. Funct. Anal. 143, No. 2, 337--348 (1997; Zbl 0959.47005)] that originally involved only one matrix.
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 2012715
zbMATH Keywords: matrix inequality
zbMATH Keywords: arithmetic-geometric mean inequality
zbMATH Keywords: trace inequality
zbMATH Keywords: singular value
zbMATH Keywords: norm inequality
zbMATH Keywords: Weyl's monotonicity principle
reviewed by: Frank Uhlig
MaRDI profile type: Publication
full work available at URL: j.laa.2003.08.008
OpenAlex ID: W2083086204
cites work: An inequality for a sum of quadratic forms with applications to probability theory
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DOI: 10.1016/J.LAA.2003.08.008
description: scientific article; zbMATH DE number 2012715