Generalized reflexive matrices: Special properties and applications

The main purpose of this paper is to introduce and exploit special properties of two special classes of rectangular matrices A and B that have the relations A = PAQ and B = -PBQ, A, B epsilon C-nXm, where P and Q are two generalized reflection matrices. The matrices A (B), a generalization of reflexive (antireflexive) matrices and centrosymmetric matrices, are referred to in this paper as generalized reflexive (antireflexive) matrices. After introducing these two classes of matrices and developing general theories associated with them, we then show how to use some of the important properties to decompose linear least-squares problems whose coefficient matrices are generalized reflexive into two smaller and independent subproblems. Numerical examples are presented to demonstrate their usefulness.