Overview of W. K. Clifford's geometric algebras

Abstract

Abstract This paper presents the very basics of W. K. Clifford's geometric algebras (GAs), which encompass Euclidean GA, as well as of the most important ones for engineering, graphics, virtual reality, signal processing, encryption, neural networks (deep learning), crystallography, physics and geographic information systems etc.: quaternions, conformal GA (CGA), projective (plane) GA (PGA), space-time GA and spinor algebras for physics, quantum register algebra (QRA) for qubit computations and algebras for computing with conics and quadrics. This article is part of the theme issue ‘Modern applications of geometric algebra’.