双曲型交换四元数的极表示

孔祥强

doi:10.3969/j.issn.1000-5641.201911001

双曲型交换四元数的极表示

doi: 10.3969/j.issn.1000-5641.201911001

孔祥强

菏泽学院数学与统计学院, 山东菏泽　274015

基金项目: 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)

详细信息

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: kong3058@126.com

中图分类号: O153.3
计量
- 文章访问数: 72
- HTML全文浏览量: 81
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2018-12-19
- 网络出版日期: 2019-12-25
- 刊出日期: 2020-01-01

The polar form of hyperbolic commutative quaternions

KONG Xiangqiang

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

摘要

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$e_1 -e_2 $表示及矩阵表示形式; 其次, 给出了双曲型交换四元数的极表示定理, 并证明了极表示的存在性与唯一性, 得到双曲型交换四元数极表示的系列性质; 最后, 探讨了双曲型交换四元数的极表示与$e_1 -e_2 $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.
- 双曲型交换四元数 /
- 极表示 /
- 矩阵表示 /
- 范数 /
- 行列式
Abstract: Firstly, this paper presents the $e_1 -e_2 $ 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, $e_1 -e_2$ 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.
- hyperbolic commutative quaternion /
- polar form /
- matrix representation /
- norm /
- determinant

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参考文献(16)

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