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http://dx.doi.org/10.4134/BKMS.2009.46.3.511

ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD = E  

Dehghan, Mehdi (DEPARTMENT OF APPLIED MATHEMATICS FACULTY OF MATHEMATICS AND COMPUTER SCIENCE AMIRKABIR UNIVERSITY OF TECHNOLOGY)
Hajarian, Masoud (DEPARTMENT OF APPLIED MATHEMATICS FACULTY OF MATHEMATICS AND COMPUTER SCIENCE AMIRKABIR UNIVERSITY OF TECHNOLOGY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 511-519 More about this Journal
Abstract
A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.
Keywords
anti-reflexive matrix; generalized reflection matrix; matrix equation; reflexive inverse; reflexive matrix;
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