Author(s)

Gang Wang^1,2, Zhenwei Guo², Dong Zhang³, Tongsong Jiang^1,2,3*

¹School of Mathematical Science, Liaocheng University, Liaocheng, China.
²School of Mathematics and Statistics, Heze University, Heze, China.
³College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China.

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.

V-Quaternion, Complex Representation, Real Representation, Linear Equations, Quaternion, Split Quaternion

Wang, G. , Guo, Z. , Zhang, D. and Jiang, T. (2019) Algebraic Techniques for Linear Equations over Quaternions and Split Quaternions: A Unified Approach in Quaternionic and Split Quaternionic Mechanics. Journal of Applied Mathematics and Physics, 7, 1718-1731. doi: 10.4236/jamp.2019.78118.