Author(s)

Zhenwei Guo¹, Gang Wang¹, Dong Zhang², Tongsong Jiang^1,2,3

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

This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.

v-Quaternion, Complex Representation, Quaternion, Split Quaternion, Eigenvalues, Eigenvectors

Guo, Z. , Wang, G. , Zhang, D. and Jiang, T. (2019) A Unified Algebraic Technique for Eigenvalues and Eigenvectors in Quaternionic and Split Quaternionic Mechanics. Journal of Applied Mathematics and Physics, 7, 1929-1940. doi: 10.4236/jamp.2019.79133.