A Construction of Matrix Representation of Clifford Algebras

Abstract

In this paper, we introduce a construction to obtain matrix algebras , which are isomorphic to the real Clifford algebras for some p and q with n = p + q. The vector generators for the matrix algebra are totally different from the vector generators of L (0),n, which is isomorphic to , constructed in [4]. Moreover, we present the invertibility of a linear combination of generators in . This can give another tool to classify the Clifford algebra in the sense of generators.