The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics
type: Item
instance of: scholarly article
title: The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics
zbMATH Open document ID: 1071.15014
author: Xian Zhang
published in: Journal of Multivariate Analysis
publication date: 2005-05-12T00:00:00Z
review text: The author obtains necessary and sufficient conditions for the solvability of the couple of matrix equations \(AXA^*=BB^*\) and \(CXC^*=DD^*\) where the solution \(X\) must be Hermitian nonnegative-definite. A representation of the general common such solution (when it exists) is given. Thus the author solves a statistical problem concerned when testing linear hypotheses about regression coefficients in the multivariate linear model. He corrects a result of \textit{D.M. Young, J.W. Seaman Jr.} and \textit{L.M. Meaux} [J. Multivariate Anal. 68, No.2, 165-175 (1999; Zbl 0927.62057)] which has been proved to be wrong in \textit{J. Groß} [Linear Algebra Appl. 321, 123-129 (2000; Zbl 0984.15011)].
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62K15
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 2167800
zbMATH Keywords: Hermitian (symmetric) nonnegative-definite solution
zbMATH Keywords: Hermitian (symmetric) positive-definite solution
zbMATH Keywords: matrix equation
zbMATH Keywords: kernel space
zbMATH Keywords: column space
zbMATH Keywords: Moore-Penrose generalized inverse
zbMATH Keywords: linear hypothesis
zbMATH Keywords: multivariate linear model
zbMATH Keywords: regression
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.jmva.2004.04.009
OpenAlex ID: W2056008400
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DOI: 10.1016/J.JMVA.2004.04.009
description: scientific article; zbMATH DE number 2167800