P-(skew)symmetric common solutions to a pair of quaternion matrix equations

An n × n quaternion matrix A is termed P-symmetric (or P-skewsymmetric) if A = PAP (or A = − PAP), where P is an n × n nontrivial quaternion involution. In this paper, we first establish necessary and sufficient conditions for the existence and the expression of the general solution to the system of...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 195; no. 2; pp. 721 - 732
Main Authors: Wang, Qing-Wen, Chang, Hai-Xia, Lin, Chun-Yan
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.02.2008
Elsevier
Subjects:
Algebra
Exact sciences and technology
Finite differences and functional equations
Functional analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Moore–Penrose inverse
Numerical analysis
Numerical analysis. Scientific computation
P-skewsymmetric matrix
P-symmetric matrix
Quaternion matrix
Sciences and techniques of general use
System of matrix equations
P-symmetric matrix
Quaternion matrix
Moore–Penrose inverse
P-skewsymmetric matrix
System of matrix equations
Numerical analysis
Necessary and sufficient condition
Moore Penrose inverse
Applied mathematics
Symmetric matrix
Matrix equation
Moore-Penrose inverse
Equation system
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:An n × n quaternion matrix A is termed P-symmetric (or P-skewsymmetric) if A = PAP (or A = − PAP), where P is an n × n nontrivial quaternion involution. In this paper, we first establish necessary and sufficient conditions for the existence and the expression of the general solution to the system of quaternion matrix equations A 1 X 1 = C 1 , A 2 X 2 = C 2 , A 3 X 1 B 1 + A 4 X 2 B 2 = C b , then use the results on the system mentioned above to give necessary and sufficient conditions for the existence and the representations of P-symmetric and P-skewsymmetric solutions to the system of quaternion matrix equations A a X = C a and A b XB b = C b . Furthermore, we establish representations of P-symmetric and P-skewsymmetric quaternion matrices. A numerical example is presented to illustrate the results of this paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.05.021