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’.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Advanced Algebra and Geometry
Holomorphic and Operator Theory
Publication details
- Journal / source
- Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
- Publisher
- The Royal Society
- Volume
- 384
- Issue
- 2326
- Publication date
- 13 August 2026
- Language
- EN