Cramer’s rules for the system of quaternion matrix equations with η -Hermicity

• Published in: 4Open Vol. 2; p. 24
• Main Author: Kyrchei, Ivan I.
• Format: Journal Article Book Review
• Language: English
• Published: Les Ulis Cedex EDP Sciences 2019
• Subjects: Cramer rule; Generalized inverse; Noncommutative determinant; Projectors; Quaternion matrix; Signal processing; System of matrix equations; η-Hermicity
• ISSN: 2557-0250; 2557-0250
• DOI: 10.1051/fopen/2019021

The system of two-sided quaternion matrix equations with η -Hermicity, A 1 XA 1 η* = C 1 , A 2 XA 2 η* = C 2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η -Hermitian solution when C 1 = C η* 1 and C 2 = C η* 2 and for an η -skew-Hermitian solution when C 1 = − C η* 1 and C 2 = − C η* 2 are also explored.