The Moore-Penrose Inverses of Clifford Algebra Cℓ_1,2

2022/04/23 by Cao, Wensheng, Zheng, Ronglan, Cao, Huihui · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2204.11047

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.

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