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

• 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
• DOI: 10.1016/j.amc.2007.05.021

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.