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- Title
以分裂四元数的概念为依托,首先给出了分裂四元数的代数性质;其次,得到了不同情形下分裂四元数的棣莫弗定理和欧拉公式;进一步,依据所得棣莫弗定理,得到分裂四元数方程的求根定理,得出求分裂四元数的任意方幂的公式,并研究了分裂四元数不同方幂之间的联系;最后,给出分裂四元数的实表示矩阵的棣莫弗定理.利用数值算例验证了结论的正确性和有效性.
- Authors
孔祥强
- Abstract
Relying on the concept of split quaternions, firstly, the algebraic properties of split quaternions are given; secondly, the De Mover's theorem and Euler formula of split quaternions in different situations are obtained; further, based on the obtained De Moffer The theorem, the root theorem of the split quaternion equation is obtained, the formula for finding the arbitrary power of the split quaternion is obtained, and the relationship between the different powers of the split quaternion is studied; finally, the split quaternion is given The real representation of the matrix Demover's theorem. Numerical examples are used to verify the correctness and validity of the conclusion.
- Subjects
EULER theorem; QUATERNIONS; EQUATIONS
- Publication
Journal of Central China Normal University, 2021, Vol 55, Issue 1, p18
- ISSN
1000-1190
- Publication type
Article
- DOI
10.19603/j.cnki.1000-1190.2021.01.004