Equality conditions for matrix Kantorovich-type inequalities
type: Item
instance of: scholarly article
title: Equality conditions for matrix Kantorovich-type inequalities
zbMATH Open document ID: 0882.15018
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-08T00:00:00Z
review text: Following a paper of \textit{S. Liu} and \textit{H. Neudecker} [ibid. 197, No. 1, 23-26 (1996; Zbl 0853.15014)], the authors present sufficient and necessary conditions under which equality occurs in matrix Kantorovich-type inequalities. They also present several relevant inequalities. The following concluding comments are stated. (i) By using the results of Section 3, one can examine the special cases for the Hadamard product, and for the upper-left submatrices. (ii) Applying the black-method, plenty of results for several cases of sums of matrices including Kantorovich and Cauchy-Schwarz inequalities can be easily derived from the results in this paper. (iii) Only the case which involves one positive definite matrix is considered in Section 3.
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 1053999
zbMATH Keywords: positive definite matrix
zbMATH Keywords: equality conditions
zbMATH Keywords: matrix Kantorovich-type inequalities
zbMATH Keywords: Hadamard product
zbMATH Keywords: Cauchy-Schwarz inequalities
author: Shuangzhe Liu
author: Wolfgang Polasek
author: Heinz Neudecker
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5526
OpenAlex ID: W2062527268
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DOI: 10.1006/JMAA.1997.5526
description: scientific article; zbMATH DE number 1053999