Algebraic Techniques for Linear Equations over Quaternions and Split Quaternions: A Unified Approach in Quaternionic and Split Quaternionic Mechanics

• 作者: Dong Zhang Gang Wang Tongsong Jiang Zhenwei Guo
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: V-Quaternion Complex REPRESENTATION Real REPRESENTATION Linear Equations QUATERNION SPLIT QUATERNION
• 年，卷（期）: 2019,（8）
• 页码范围: 1718-1731
• 页数: 14页
• 分类号: O1

摘要

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.