1. The Moore-Penrose Inverses of Clifford Algebra $C\ell_2$
- Author
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Zheng, Rong lan, Cao, Wen sheng, and Cao, Hui hui
- Subjects
Mathematics::Functional Analysis ,Statistics::Machine Learning ,Rings and Algebras (math.RA) ,FOS: Mathematics ,Mathematics - Rings and Algebras - Abstract
In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_2$ and a ring of matrices, and represent the elements in $C\ell_2$ by real matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra $C\ell_2$. we solve the linear equation $axb=d$, $ax=xb$ and $ax=\bar{x}b$. We also obtain necessary and sufficient conditions for two numbers in $C\ell_2$ to be similar and pseudosimilar., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2204.11047
- Published
- 2022
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