Solvability of a quaternion matrix equation
type: Item
instance of: scholarly article
title: Solvability of a quaternion matrix equation
zbMATH Open document ID: 1020.15014
author: Cao Wensheng
published in: Applied Mathematics. Series B (English Edition)
publication date: 2003-06-17T00:00:00Z
review text: The author studies the solvability of the matrix equations \((*)\) \(AXB=D\) and \((**)\) \(A^*X^*B^*\pm BXA=D\) where \(A\), \(B\), \(D\) are quaternion matrices. He gives necessary and sufficient conditions for the solvability of \((*)\) (resp. of \((**)\)) in Hermitian and in skew-Hermitian matrices (resp. in quaternion matrices), and he presents formulas for the general solutions when the conditions are met. These formulas involve the matrices \(A\), \(B\), \(D\) and their Moore-Penrose inverses. (The Moore-Penrose inverse \(A^+\) of the \(m\times n\) quaternion matrix \(A\) is an \(n\times m\)-matrix \(X\) satisfying the conditions \(AXA=A\), \(XAX=X\), \((AX)^*=AX\), \((XA)^*=XA\).).
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1877156
zbMATH Keywords: quaternion matrix
zbMATH Keywords: (skew)-Hermitian matrix
zbMATH Keywords: (quaternion) matrix equation
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: general solutions
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: s11766-996-0015-2
OpenAlex ID: W2069315805
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DOI: 10.1007/S11766-996-0015-2
description: scientific article; zbMATH DE number 1877156