The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
type: Item
instance of: scholarly article
title: The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
zbMATH Open document ID: 1050.15016
DOI: 10.1016/S0024-3795(03)00607-4
author: Xiyan Hu
author: Zhen-Yun Peng
published in: Linear Algebra and its Applications
publication date: 2003-12-04T00:00:00Z
review text: Let \(P\in\mathbb{C}^{n\times n}\) be both Hermitian and unitary. A matrix \(X\in\mathbb{C}^{n\times n}\) is said to be reflexive (resp. anti-reflexive) with respect to \(P\) when \(X= PXP\) (resp. \(X = -PXP\)). Conditions are given for existence of reflexive and antireflexive solutions (with respect to \(P\)) of the equation (1) \(AX= B\), where \(A,B\in\mathbb{C}^{m\times n}\) are given matrices. If \(X_0\in \mathbb{C}^{n\times n}\) is a given matrix, expressions are given for the reflexive and anti-reflexive solutions of (1) which are the nearest to \(X_0\) in the Frobenius norm.
reviewed by: Mihail M. Konstantinov
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 2013049
zbMATH Keywords: Reflexive matrix
zbMATH Keywords: Anti-reflexive matrix
zbMATH Keywords: Matrix equation
zbMATH Keywords: Matrix nearness problem
zbMATH Keywords: reflexive solutions
zbMATH Keywords: anti-reflexive solutions
zbMATH Keywords: Frobenius norm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013049