The Principle of Duality in Clifford Algebra and Projective Geometry

Abstract

A completely dual approach to Clifford algebra is presented in this article. It leads to the introduction of two new products, the dual geometric product * and the dual inner product o, and sheds new light on the duality relation between the progressive and regressive outer products of the Clifford algebra. On the firm base of this dual approach, the projective principle of duality is formulated in this completeness for the first time in the language of Clifford algebra. In order to provide mathematical concepts which are close to possible applications in theoretical physics, section 5 is devoted to projective coordinate systems. The incidence relations between the primitive geometric forms, the linear complex, and Desargues’ theorem are discussed as well.