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

doi:10.3969/j.issn.1000-5641.2022.06.002

Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (6): 8-16.doi: 10.3969/j.issn.1000-5641.2022.06.002

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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

Abstract

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

CLC Number:

O153.3

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.

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

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