The general common nonnegative-definite and positive-definite solutions to the matrix equations \(AXA^ *=BB^ *\) and \(CXC^ *=DD^ *\).
type: Item
instance of: scholarly article
title: The general common nonnegative-definite and positive-definite solutions to the matrix equations \(AXA^ *=BB^ *\) and \(CXC^ *=DD^ *\).
zbMATH Open document ID: 1062.15009
DOI: 10.1016/S0893-9659(04)90123-1
author: Xian Zhang
author: Mei-yu Cheng
published in: Applied Mathematics Letters
publication date: 2005-02-25T00:00:00Z
review text: The authors give necessary and sufficient conditions for the existence of a common nonnegative-definite (positive-definite) solution to the pair of matrix equations \(AXA^*=BB^*\) and \(CXC^*=DD^*\). In the case of existence they give the representation of the general common solution of this type. The paper is supplementary to this one of \textit{D. M. Young}, \textit{J. W. Seaman} and \textit{L. M. Meaux} [J. Multivariate Anal. 68, 165--175 (1999; Zbl 0927.62057)] after a mistake in the latter paper has been indicated by \textit{J. Groß} [Linear Algebra Appl. 321, 123--129 (2000; Zbl 0984.15011)]. The authors present an example illustrating the advantage of their approach.
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 2138620
zbMATH Keywords: nonnegative-definite solution
zbMATH Keywords: positive-definite solution
zbMATH Keywords: generalized inverse
zbMATH Keywords: nullspace
zbMATH Keywords: column space
zbMATH Keywords: pair of matrix equations
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
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full work available at URL: s0893-9659(04)90123-1
OpenAlex ID: W1992201645
description: scientific article; zbMATH DE number 2138620