ABSTRACT
This chapter describes the “Clifford algebra” that integrates the Hamilton algebra in Chapter 4 and the Grassmann algebra in Chapter 5, using a new operation called “geometric product.” We first state the operational rule of the geometric product to show that the inner and outer products of vectors and the quaternion product can be computed using the geometric product. The important fact is that vectors and k-vectors have their inverse with respect to the geometric product. We show how the projection, rejection, reflection, and rotation of vectors are described using the geometric product and point out that orthogonal transformations of the space can be described in the form of “versors.”
