Generalized Reflexive Matrices: Special Properties and Applications

Authors:
Hsin-Chu Chen
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1998

Citing 0
Cited 13

The solvability conditions for the inverse eigenvalue problems of reflexive matrices

Journal of Computational and Applied Mathematics
The reflexive and anti-reflexive solutions of the matrix equation AHXB=C

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Generalized reflexive solutions of the matrix equation AXB=D and an associated optimal approximation problem

Computers & Mathematics with Applications
Procrustes problems for (P,Q,η)-reflexive matrices

Journal of Computational and Applied Mathematics
The solvability conditions for the inverse eigenvalue problems of reflexive matrices

Journal of Computational and Applied Mathematics
The left and right inverse eigenvalue problems of generalized reflexive and anti-reflexive matrices

Journal of Computational and Applied Mathematics
Dykstra's algorithm for constrained least-squares doubly symmetric matrix problems

Theoretical Computer Science
On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations

International Journal of Systems Science
An inverse eigenproblem and an associated approximation problem for generalized reflexive and anti-reflexive matrices

Journal of Computational and Applied Mathematics
Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1+A2X2B2=C

Mathematical and Computer Modelling: An International Journal
An efficient algorithm for solving general coupled matrix equations and its application

Mathematical and Computer Modelling: An International Journal
The reflexive least squares solutions of the matrix equation $A_1X_1B_1+A_2X_2B_2+\cdots +A_lX_lB_l=C$with a submatrix constraint

Numerical Algorithms
Efficient iterative solutions to general coupled matrix equations

International Journal of Automation and Computing

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Abstract

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 {\rm and} B = -PBQ, \qquad A, B \in {\cal C}^{n \times m}, 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.