Geometric Algebra in 3 Dimensions
In this lecture we explore the consequences of our definition of the geometric product in three dimensions. We find that Hamilton’s quaternions arise naturally in the geometric algebra of three dimensions, but that the generators of the algebra do not represent vectors, instead they represent planes.
In the final part of the lecture we start to look at reflections and rotations, and introduce the fundamental concept of the rotor – the generator of rotations in a geometric algebra.