Mathematics

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

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

Received date: 2021-01-22

  Online published: 2022-11-22

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.

Cite this article

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 . DOI: 10.3969/j.issn.1000-5641.2022.06.002

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