The (P,Q) Reflexive and Anti-reflexive Solutions of the Matrix Equation AX = B

被引：0

作者：

Zhang, Jian-Chen ^{[1
]}

Zhou, Shu-Zi ^{[1
]}

Hu, Xi-Yan ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Peoples R China

来源：

ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL II: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS | 2008年

关键词：

(P; Q) reflexive matrix; Q) anti-reflexive matrix; Matrix equation; Matrix nearness Problem;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An n x n complex matrix P is said to be a generalized reflection matrix if P-H = P and P-2 = 1. An n x n complex matrix A is said to be a (P,Q) reflexive (or anti-reflexive) matrix with respect to the generalizedreflection matrix dual (P,Q) if A = PAQ (or A = -PAQ). This paper establishes the necessary and sufficient conditions for the existence of and the expressions for the (P,Q) reflexive and anti-reflexive 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 has been provided.

引用

页码：433 / 436

页数：4

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