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arXiv · 2204.11047

The Moore-Penrose Inverses of Clifford Algebra $C\ell_{1,2}$

Wensheng Cao·Ronglan Zheng·Huihui Cao
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Abstract

In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_{1,2}$ and a ring of matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra $C\ell_{1,2}$. Using the Moore-Penrose inverse, we solve the linear equation $axb=d$ in $C\ell_{1,2}$. We also obtain necessary and sufficient conditions for two numbers in $C\ell_{1,2}$ to be similar.

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Wensheng Cao, Ronglan Zheng, Huihui Cao. 2022-04-23. The Moore-Penrose Inverses of Clifford Algebra $C\ell_{1,2}$. https://arxiv.org/abs/2204.11047

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