Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations

• Published in: Computers & mathematics with applications (1987) Vol. 55; no. 6; pp. 1142 - 1147
• Main Authors: Li, Yao-tang, Wu, Wen-jing
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2008
• Subjects: Algebra; Criteria; Inner inverse; Mathematical analysis; Mathematical models; Quaternions; Real quaternion algebra; Reflexive inverse; Symmetric and skew-antisymmetric matrix; System of quaternion matrix equations; Real quaternion algebra; System of quaternion matrix equations; Reflexive inverse; Symmetric and skew-antisymmetric matrix; Inner inverse
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2007.06.015

In this paper we consider symmetric and skew-antisymmetric solutions to certain matrix equations over the real quaternion algebra H . First, a criterion for a quaternion matrix to be symmetric and skew-antisymmetric is given. Then, necessary and sufficient conditions are obtained for the matrix equation A X = C and the following system { A 1 X = C 1 X B 3 = C 3 to have symmetric and skew-antisymmetric solutions. The expressions of such solutions of the matrix equation and the system mentioned above are also given.