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

0:00 - Introduction
2:57 - Grassmann Algebras (wedge product)
13:20 - Clifford Algebras
22:45 - Grassman vs Clifford Algebras
26:35 - Abstract definitions of Algebras

[eigenchris]

Error at 19:17: each of "i", "j", and "k" should have a minus sign in front. I got it correct in video 6.1, but got it wrong here for some reason.

[MarceloUmeda]

Chris, this was by far the best explanation of Clifford Algebra I've come across. Sudgylacmoe is also sensational, but your systematic treatment filled so many gaps in my understanding. Thank you so much!

[AllemandInstable]

this channel is a complete banger
feels even more impressive when a physicist gives you mathematical insight

[SzTz]

You are such a talented Physicist, better than any university course.

[MarceloRobertoJimenez]

I've been trying to make sense of all these concepts for years. This video does the job in half an hour. Congratulations!

[GeoffryGifari]

greatly appreciate your effort to decompose a concept this advanced step-by-step

[theidioticbgilson]

POG POG POG POG!!!

eigenchris clifford algebra just dropped!!! let's fucking

[kashu]

this is the episode i have looked most forward to

[Globbo_The_Glob]

Your videos have changed how I see physics and have helped me learn exterior topics because I have this as a basis. I can't say how much I appreciate the effort you put out here.

[eric]

awesome content dude! You are so good at breaking things down into clear and small steps!

[DN-psbn]

You know what, I jumped straight into this video without going from video 1. I had to do a lot of reading to catch up. I’ll go back and learn those videos and come back to this one.

[jimlbeaver]

Definitely one of your better explanations! You are getting really good at this…please keep it up. I’m learning a lot thanks

[makespace]

Another outstandingly clear and understandable production!

[CrucialFlowResearch]

If you like Clifford algebras, you'll like Grassmann.jl my computer algebra implementation for the Julia language

[Waltonruler]

Excited to be getting to this! I've been reading Doran and Lasenby's text on this stuff, but the specific applications to quantum mechanics has still left me a bit mystified. Your videos are so clear, I'm sure it'll help me grok the physics better

[wafikiri_]

Maxwell's famous equations were not four but twenty. But the introduction of the vector operator nabla let us reduce them to just four. It is nice to see they are but aspects of just one, and it makes much sense: one law for one major part of Physics, electromagnetism. I'd be glad to learn which those for the strong and weak forces are.

[francoisfjag]

brilliant. Best video ever introducing Clifford algebras.

[iqdx]

Simply the most useful playlist on this difficult topic that I have found in the last few years. Congratulations and thank you for your work. I do look forward to tracking the upcoming episodes to the very end!

[junghoonkwon]

what a clear and accecible lecture on clifford algebra!!

[nice]

This is great! I haven't seen an explaination of the abstract tensor quotient rule with this clarity