On matrix trace inequalities and related topics for products of Hermitian matrices
type: Item
instance of: scholarly article
title: On matrix trace inequalities and related topics for products of Hermitian matrices
zbMATH Open document ID: 0815.15013
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-07-09T00:00:00Z
review text: An alternate proof of a simple matrix trace inequality of \textit{R. Bellman} [ISNM 47, 89-90 (1980; Zbl 0433.15011)] and \textit{Y. Yang} [J. Math. Anal. Appl. 133, No. 2, 573-574 (1988; Zbl 0651.15018)] is put forward, namely: For positive semidefinite matrices \(A,B\) of the same order, we have \(0 \leq \text{tr} (AB) \leq \text{tr} (A) \text{tr} (B)\). Besides, two theorems on the eigenvalues of two matrices \(A,B\) are proved, namely: (1) If \(A\) and \(B\) are both positive definite, then the eigenvalues of \(AB\) are positive; (2) If \(A,B\) are both Hermitian and of the same order, then the trace of \(AB\) is real.
reviewed by: Yang Yingchen
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 720414
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: positive semidefinite matrix
zbMATH Keywords: matrix trace inequality
zbMATH Keywords: eigenvalues
author: Ian D. Coope
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1475
OpenAlex ID: W2060541368
DOI: 10.1006/JMAA.1994.1475
description: scientific article; zbMATH DE number 720414