References and software

Publications and websites

A captivating review article:
[1] – The vector algebra war: a historical perspective ( James M. Chappell, Azhar Iqbal, John G. Hartnett, and Derek Abbott

[2] – Visual complex analysis – Tristan Needham, Oxford University Press
Text sui generis published in 1997 which presents in visual form many results of complex analysis, in the wake of the geometric approach to calculus, developed by Newton in his Principia.

Alan Macdonald has published two texts that have the merit of integrating the basics of geometric algebra in the context of a conventional treatment of linear algebra and vector calculus. However, these are two texts with a formal approach, very little intuitive and they are suitable for those who already know those topics:
[3] – Linear and geometric algebra and related video series on YouTube
[4] – Vector and Geometric Calculus and related video series on YouTube

[5] – Geometric algebra primer – Jaap Suter http: // www / geometric-algebra

[6] – Geometric algebra for computer science – website by Leo Dorst , Danil Fontijne and Stephen Mann accompanying the text of the same name, which is a reference point for the computer applications of GA.

[7] – Geometric algebra for physicists – Chris Doran & amp; Anthony Lasenby – Cambridge university press
Reference text for the application of GA to physics. It is the elaboration of the works developed since the 1960s by Hestenes, the true rediscoverer of these ideas in the twentieth century.

[8] – New foundations of classical mechanics – David Hestenes
A book by the mathematician who had the great merit of rediscovering the AG and proposing it again in an effort of its whole academic life. The text is a bit old style, that is, very few figures and many exercises (to do!)
It complements well with the book [7] of the Cambridge group.

[9] – Geometric algebra and applications to physics – Venzo de Sabbata & amp; Bidyut Kumar Datta
Text mainly dedicated to the applications of GA in quantum mechanics.

[10] – Spacetime algebra as a powerful tool for electromagnetism (
by Justin Dressel, Konstantin Bliokh and Franco Nori
A comprehensive review on the formalism of geometric algebra applied to electromagnetism.
The introductory part is very clear and well done, then the difficulty of the article quickly increases.

[11] – Electromagnetic fields with geometric algebra by Mauro Mongiardo, Giuseppina Monti, Tullio Rozzi and Giuseppe Venanzoni
The text – rich in listings in wxMaxima – uses Pauli’s matrices as a computational tool to deploy the power and simplicity of geometric algebra in the treatment of electromagnetic fields.

[12] – Eckhard Hitzer: Geometric Algebra playlist (YouTube, 18 videos)


GAViewer – calculation and visualization software supplied with the book [6] – Geometric algebra for computer science

Galgebra – originally developed by Alan Bromborsky and currently maintained and developed by the PGAE (pythonic geometric algebra enthusiasts). It is a python module for the symbolic computation of geometric algebra.

Ganja – by Steven de Keninck – javascript generator of geometric algebras with different metric signature, with graphic representation capabilities