TITLE:
Algebraic Techniques for Linear Equations over Quaternions and Split Quaternions: A Unified Approach in Quaternionic and Split Quaternionic Mechanics
AUTHORS:
Gang Wang, Zhenwei Guo, Dong Zhang, Tongsong Jiang
KEYWORDS:
V-Quaternion, Complex Representation, Real Representation, Linear Equations, Quaternion, Split Quaternion
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.8,
August
16,
2019
ABSTRACT: This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.