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

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.

13 pages, 8 references