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

Abstract

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