The Moore-Penrose Inverses of Clifford Algebra C2
Abstract
In this paper, we introduce a ring isomorphism between the Clifford algebra C2 and a ring of matrices, and represent the elements in C2 by real matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra C2. we solve the linear equation axb=d, ax=xb and ax=xb. We also obtain necessary and sufficient conditions for two numbers in C2 to be similar and pseudosimilar.
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