The polar form of hyperbolic commutative quaternions

KONG Xiangqiang

doi:10.3969/j.issn.1000-5641.201911001

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Jan. 2020

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KONG Xiangqiang. The polar form of hyperbolic commutative quaternions[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 16-23. doi: 10.3969/j.issn.1000-5641.201911001

Citation:

KONG Xiangqiang. The polar form of hyperbolic commutative quaternions[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 16-23. doi: 10.3969/j.issn.1000-5641.201911001

KONG Xiangqiang. The polar form of hyperbolic commutative quaternions[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 16-23. doi: 10.3969/j.issn.1000-5641.201911001

Citation:

KONG Xiangqiang. The polar form of hyperbolic commutative quaternions[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 16-23. doi: 10.3969/j.issn.1000-5641.201911001

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The polar form of hyperbolic commutative quaternions

doi: 10.3969/j.issn.1000-5641.201911001

KONG Xiangqiang

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

Received Date: 2018-12-19
Available Online: 2019-12-25
Publish Date: 2020-01-01

Abstract

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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References(16)

References

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