The reflexive and anti-reflexive solutions of the matrix equation AX= B

An n× n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2= I. An n× n complex matrix A is said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix P if A= PAP (or A=− PAP). This paper establishes the necessary and sufficient...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2003-12, Vol.375, p.147-155
Main Authors: Peng, Zhen-yun, Hu, Xi-yan
Format: Article
Language:English
Subjects:
Algebra
Anti-reflexive matrix
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Matrix equation
Matrix nearness problem
Reflexive matrix
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An n× n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2= I. An n× n complex matrix A is said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix P if A= PAP (or A=− PAP). This paper establishes the necessary and sufficient conditions for the existence of and the expressions for the reflexive and anti-reflexive with respect to a generalized reflection matrix P solutions of the matrix equation AX= B. In addition, in corresponding solution set of the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm have been provided.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(03)00607-4