Complex Eigenvalues in Geometric Algebra

Introduction A less well-known features of Twitter is that, outside of all the angry shouting, occasionally an interesting mathematical discussion breaks out. One of these was started by asking the simple question `is there a geometric interpretation of complex eigenvalues?’. … Continued

Euclidean Geometry and Geometric Algebra

Image showing a motor orbit. Code available at If you prefer, you can download a PDF version of this article, slightly expanded with better typesetting. Introduction Geometric algebra is a very natural language for describing concepts in Euclidean geometry, … Continued

Geometric Algebra in Haskell

Slides from a talk delivered at the 2017 Haskell Exchange on expressing geometric algebra in the functional programming language Haskell. Haskell Exchange Slides

GA 2016 – Lecture 9

Unification In this final set of slides  we complete the story of how conformal geometric algebra unifies many of the classical geometries, covering Euclidean, spherical, hyperbolic (non-Euclidean), projective and inversive geometries. Rotors are shown to generate rotations, translations and special … Continued

GA 2016 – Lecture 8

Conformal Geometric Algebra It is only fairly recently that we realised just how powerful the combination of conformal geometry and geometric algebra could be as a tool for understanding Euclidean geometry. The key ideas were introduced around 2000, and have led … Continued

GA 2016 – Lecture 7

Implementation In this lecture we discuss the practicalities of implementing geometric algebra in your own code. We start by looking at the various possibilities for data structures to encode a multivector, looking at the pros and cons of various solutions … Continued

Symbolic Algebra and GA

A number of different groups have produced implementations of Geometric Algebra in symbolic algebra packages. These include: A Mathematica notebook created by Terje Vold. Clifford Algebra with Mathematica, by  Aragon-Camarasa, et al. arXiv:0810.2412 A GA module for SymPy. SymPy is a … Continued

GA 2016 – Lecture 6

Geometric Calculus In this lecture we introduce the core concept of the vector derivative. This is the natural extension of the gradient operator to geometric algebra setting, where it inherits the properties of a grade-1 vector. The separate inner and outer … Continued

GA 2016 – Lecture 5

Spacetime Algebra In this lecture we introduce the geometric algebra of Minkowski spacetime, or spacetime algebra. Historically spacetime algebra drove much of the early interest in geometric algebra, and this importance was recently celebrated in a new edition of David Hestenes’ … Continued

GA2016 – Lecture 4

Algebraic Foundations and 4D In this lecture we set out the algebraic rules that define a geometric algebra in spaces of arbitrary dimensions. The inner and outer products are extended to their most general definition, and we look at rotors … Continued

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