Geometric Algebra vs. Clifford Algebra

Показать описание

In this short, I talk about the differences, if any, between geometric algebra and Clifford algebra. While some consider them distinct mathematical objects, I consider them to be identical. However, in practice, the way people use these two objects is quite distinct, and you can't just ignore these distinctions.

Patreon Supporters:
Christoph Kovacs
David Johnston
Jason Killian
LoganMP
p11
Richard Penner
Rosario

sudgylacmoe

Рекомендации по теме

Комментарии

You know something is useful when you can look at it from multiple perspectives.

caspermadlener

Geometric Algebras are quadradic rings and Clifford Algebras are a Big Red Dog.

pacotaco

Geometric algebra was a curiosity for a while. Guess I need to study it now.

curiousaboutscience

You are the only one that I found talking about that❤

santykachu

Something I've run into is that two different professors such as Professor Tisza and Professor Hestenes can refer to Geometric Algebra but they are not using the same notation. This is one reason why Professor Hestenes appropriated the name Geometric Algebra to distinguish his multivector formalism from Clifford Algebra. He wrote about this a lot. It involves concepts as well as notation because he is creating a unified system for both physics and math work.

BlueGiant

So in ypur book, we can talk about a geometric algebra over a finite field?

dwrchschr

So if they're not equal, they're at least isomorphic?

rtg_onefourtwoeightfiveseven

Glad you're finally addressing the allegations

justynpryce

The only difference I ever saw was in how people used the models they constructed from an algebra. Essentially an ontology layer... which isn't really the mathematics.

I've treated them as the same and only use one term over the other to keep the peace.

AlfredDiffer

I found your channel
Do you have any lessons on the topic?😊

TheDead-tg

Why do I see Cl(a, b) and G(a, b, c) or E(a, b, c) ?

dadsquadmusic

Ok. My understanding was that Clifford's algebra is subset cause there are more GAs

pavelperina

Geometric Algebra vs. Clifford Algebra

Geometric Algebra vs. Clifford Algebra

Good geometric algebra textbooks (Clifford algebras)

Spinors for Beginners 11: What is a Clifford Algebra? (and Geometric, Grassmann, Exterior Algebras)

A Swift Introduction to Geometric Algebra

Solution Strategies for Geometric (Clifford) Algebra Problems

From Zero to Geo Introduction (Geometric Algebra Series)

Self-Study Geometric Algebra!

This algebra describes EVERYTHING.

The fascinating absurdity of Geometric Algebra

A Swift Introduction to Projective Geometric Algebra

Biquaternions and the Clifford algebra CL(2) (Video 4/14).

Clifford Algebras and Time Loops

An Overview of the Operations in Geometric Algebra

Geometric Algebra in 2D - Fundamentals and Another Look at Complex Numbers

The power of Geometric Algebra Computing for Mathematica

GAME23 Johannes Branstetter - Geometric Clifford Algebra Networks

Geometric Algebra and Tensors

Jonathan Blow Explains Geometric Algebra

Geometric Algebra -- What is area? | Wedge product, Exterior Algebra, Differential Forms

A Swift Introduction to Spacetime Algebra

March 9th: Fun Applications of Geometric Algebra! by Logan Lim

Constructing Geometric Algebra

Why Geometric Algebra Should be in the Standard Linear Algebra Curriculum by Logan Lim

Introduction to Geometric (Clifford) Algebra.