双曲分裂四元数表示矩阵的棣莫弗定理

doi:10.3969/j.issn.1000-5641.2022.06.002

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (6): 8-16.doi: 10.3969/j.issn.1000-5641.2022.06.002

双曲分裂四元数表示矩阵的棣莫弗定理

孔祥强()

菏泽学院数学与统计学院, 山东菏泽　274015

收稿日期:2021-01-22 出版日期:2022-11-25 发布日期:2022-11-22
作者简介:孔祥强, 男, 副教授, 研究方向为四元数理论及其应用. E-mail: kongxiangqiang@hezeu.edu.cn
基金资助:
山东省自然科学基金(ZR201709250116, ZR2017MA029); 菏泽学院科研基金科技计划项目(XY17KJ02); 菏泽学院大学数学课程混合式教学模式研究与实践项目(2018311)

De Moivre’s theorem for a matrix representation of hyperbolic split quaternions

Xiangqiang KONG()

School of Mathematics and Statistics, Heze University, Heze, Shandong　274015, China

Received:2021-01-22 Online:2022-11-25 Published:2022-11-22

摘要/Abstract

摘要：

研究了一类双曲分裂四元数表示矩阵的棣莫弗定理. 首先, 将对双曲分裂四元数的研究转化为对双曲分裂四元数表示矩阵的研究; 其次, 利用双曲分裂四元数的极表示, 得到双曲分裂四元数表示矩阵的3种形式的棣莫弗定理, 并对欧拉公式进行了推广; 再次, 得到双曲分裂四元数的表示矩阵方程的求根公式; 最后, 利用算例验证了所得结论的正确性.

关键词: 双曲分裂四元数, 表示矩阵, 棣莫弗定理, 欧拉公式

Abstract:

In this paper, de Moivre’s theorem for a matrix representation of a class of hyperbolic split quaternions is studied. Firstly, the study of hyperbolic split quaternions is transformed into the study of a matrix representation of hyperbolic split quaternions. Secondly, by using the polar representation of a hyperbolic split quaternion, the three forms of de Moivre’s theorem for a matrix representation of the hyperbolic split quaternion are obtained, and Euler’s formula is extended. Thirdly, the root-finding formula of the hyperbolic split quaternion matrix representation equation is obtained. Finally, the validity of the conclusions is verified with some examples.

Key words: hyperbolic split quaternion, matrix representation, de Moivre’s theorem, Euler’s formula

中图分类号:

O153.3

孔祥强. 双曲分裂四元数表示矩阵的棣莫弗定理[J]. 华东师范大学学报（自然科学版）, 2022, 2022(6): 8-16.

Xiangqiang KONG. De Moivre’s theorem for a matrix representation of hyperbolic split quaternions[J]. Journal of East China Normal University(Natural Science), 2022, 2022(6): 8-16.

参考文献 16

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双曲分裂四元数表示矩阵的棣莫弗定理

De Moivre’s theorem for a matrix representation of hyperbolic split quaternions

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