Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations

Author:

Rehman Abdur1,Kyrchei Ivan2,Ali Ilyas1,Akram Muhammad1,Shakoor Abdul3

Affiliation:

1. University of Engineering & Technology, Lahore, Pakistan

2. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NASU, Lviv, Ukraine

3. Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan-Pakistan

Abstract

Some necessary and sufficient conditions for the existence of the ?-skew-Hermitian solution quaternion matrix equations the system of matrix equations with ?-skew-Hermicity, A1X = C1, XB1 = C2, A2Y = C3, YB2 = C4, X = -X?*; Y=-Y?*, A3XA?*3 + B3YB?*3=C5, are established in this paper by using rank equalities of the coefficient matrices. The general solutions to the system and its special cases are provided when they are consistent. Within the framework of the theory of noncommutative row-column determinants, we also give determinantal representation formulas of finding their exact solutions that are analogs of Cramer?s rule. A numerical example is also given to demonstrate the main results.

Publisher

National Library of Serbia

Subject

General Mathematics

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