Geometric Algebra vs. Clifford Algebra

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.
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[@pacotaco1246]

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

[@caspermadlener4191]

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

[@TheMemesofDestruction]

So it’s not a big red dog? ^.^

[@sudgylacmoe]

twitter.com/matthras/status/1438819122482012163

[@curiousaboutscience]

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

[@dwrchschr]

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

[@sudgylacmoe]

Absolutely!

[@rtg_onefourtwoeightfiveseven]

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

[@justynpryce]

Glad you're finally addressing the allegations

[@BlueGiant69202]

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.

[@kjetil1845]

>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.
where can i read about this?

[@mastershooter64]

Clifford The Big Red Algebra

[@AlfredDiffer]

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.

[@santykachu3943]

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

[@TheDead-t1g]

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

[@dadsquadmusic]

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

[@sudgylacmoe]

Cl(a, b) and G(a, b, c) are pretty much the same notation (some people drop the later numbers if they're zero), and refer to a geometric algebra with a basis vectors squaring to 1, b basis vectors squaring to -1, and c basis vectors squaring to 0. I'm not sure what the E notation is.

[@no3339]

@@sudgylacmoeprob exterior algebra or something

[@sudgylacmoe]

That's what I thought at first, but then you wouldn't have any a, b, or c.

[@pavelperina7629]

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