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New Formula for Computing Quaternion Powers
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
Department of Basics and Engineering Sciences, Faculty of Engineering, University of Khartoum, Khartoum, Sudan
- 1 Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
- 2 Department of Basics and Engineering Sciences, Faculty of Engineering, University of Khartoum, Khartoum, Sudan
Applied Mathematics·Volume 13 (2022)·Pages 282–294·Published 17 March 2022·DOI10.4236/am.2022.133021
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Abstract
In this work, we create a new mathematical formula that computes the power of a quaternion number raised to a positive integer by reducing the real matrix of order 4 × 4 that we take to represent this quaternion number to a matrix that makes the process of multiplying this quaternion number by itself simpler. We also present a new method for computing the power of a real matrix of order 2 × 2 as an application of this formula.
KeywordsQuaternionsMatrix AlgebraKayley-Dickson Construction
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