Introduction to Geometric Algebra

Geometric algebra was initiated by W.K. Clifford over 140 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing. This introduction explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, the popular conformal model, and projective geometric algebra. Geometric algebras are ideal to represent geometric transformations in the general framework of Clifford groups (also called versor or Lipschitz groups). Geometric (algebra based) calculus allows, e.g., to optimize learning algorithms of Clifford neurons, etc.