华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 1: 16 - 23

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911001

数学

双曲型交换四元数的极表示

  • 孔祥强
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  • 菏泽学院 数学与统计学院, 山东 菏泽 274015
孔祥强,男,副教授,研究方向为四元数理论及其应用.E-mail:kong3058@126.com

收稿日期: 2018-12-19

  网络出版日期: 2020-01-13

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“线上”+“线下”混合式教学模式研究与实践项目（2018311）

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The polar form of hyperbolic commutative quaternions

  • KONG Xiangqiang
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  • School of Mathematics and Statistics, Heze University, Heze Shandong 274015, China

Received date: 2018-12-19

  Online published: 2020-01-13

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摘要

以双曲型交换四元数的概念为依托，首先给出了双曲型交换四元数的e1-e2表示及矩阵表示形式；其次，给出了双曲型交换四元数的极表示定理，并证明了极表示的存在性与唯一性，得到双曲型交换四元数极表示的系列性质；最后，探讨了双曲型交换四元数的极表示与e1-e2表示、矩阵表示之间的关系，为进一步深入研究双曲型交换四元数的应用提供了理论依据.

关键词： 双曲型交换四元数; 极表示; 矩阵表示; 范数; 行列式

本文引用格式

孔祥强 . 双曲型交换四元数的极表示[J]. 华东师范大学学报（自然科学版）, 2020 , 2020(1) : 16 -23 . DOI: 10.3969/j.issn.1000-5641.201911001

Abstract

Firstly, this paper presents the e1-e2 representation and matrix representation of hyperbolic commutative quaternions. Secondly, the polar form theorem of hyperbolic commutative quaternion is presented; the existence and uniqueness of the respective polar form are proven, and a series of properties for the hyperbolic commutative quaternion polar form are obtained. Lastly, the relationship between the polar form, e1-e2 representation and matrix representation of hyperbolic commutative quaternions are discussed. Hence, the paper provides a theoretical basis for further research on the application of hyperbolic commutative quaternions.

Key words： hyperbolic commutative quaternion; polar form; matrix representation; norm; determinant

参考文献

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