Spacetime Algebra and Line Geometry

Abstract

The hidden universal Clifford algebra structure of M₄(R) is ambiguous in the sense that this matrix algebra is the universal geometric algebra belonging to each of the real four-dimensional quadratic vector spaces R^1,3 and R^2,2. As a non-universal Clifford algebra, however, M₄(R) is a geometric algebra of the unique five-dimensional quadratic vector space R^2,3.