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arXiv · 2205.05317

The Moore-Penrose Inverses of Clifford Algebra $C\ell_2$

Rong lan Zheng·Wen sheng Cao·Hui hui Cao
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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.

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BibTeXRIS

Rong lan Zheng, Wen sheng Cao, Hui hui Cao. 2022-05-11. The Moore-Penrose Inverses of Clifford Algebra $C\ell_2$. https://arxiv.org/abs/2205.05317

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