Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
type: Item
instance of: scholarly article
title: Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
zbMATH Open document ID: 1108.15014
author: Zhong-Cheng Wu
author: Qing-Wen Wang
author: Chun-Yan Lin
published in: Applied Mathematics and Computation
publication date: 2007-01-11T00:00:00Z
review text: The authors consider the maximal and minimal ranks of the matrix function \(f(X_1,X_2)=A-A_3X_1B_3-A_4X_2B_4\) where the quaternion matrices \(X_1\), \(X_2\) are subject to the consistent systems of quaternion matrix equations \(A_1X_1=C_1\), \(X_1B_1=C_2~(*)\) and \(A_2X_2=C_3\), \(X_2B_2=C_4~(**)\). Interesting particular cases are the constrained matrix equations \(f=0\) or \(X_2=0\), \(f=0\) or \(B_1=A_1^*\), \(B_2=A_2^*\), \(f=0\), the constraints being defined by systems \((*)\) and \((**)\). As applications, they give necessary and sufficient conditions for the existence of solutions to some systems of quaternion matrix equations.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5115446
zbMATH Keywords: system of quaternion matrix equations
zbMATH Keywords: minimal rank
zbMATH Keywords: maximal rank
zbMATH Keywords: linear matrix expression
zbMATH Keywords: generalized inverse
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.amc.2006.06.012
OpenAlex ID: W1977350167
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DOI: 10.1016/J.AMC.2006.06.012
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description: scientific article; zbMATH DE number 5115446