The Moore-Penrose Inverses of Clifford Algebra $C{\ell }_2$

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.

13 pages. arXiv admin note: text overlap with arXiv:2204.11047