The polar form of hyperbolic commutative quaternions
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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
$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.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.-
Key words:
- hyperbolic commutative quaternion /
- polar form /
- matrix representation /
- norm /
- determinant
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