#geometric algebra

[peniswizard69]

My dealer: got some straight gas 🔥😛 this strain is called "geometric algebra" 😳 you'll be zonked out of your gourd 💯

Me: yeah whatever. I don't feel shit.

5 minutes later: dude I swear I'm being anti-commuted

My buddy Bivector pacing: the cross product is lying to us

[then-ponder]

Time to start a wrestle with the mathematicians

What is your favorite vector product

Geometric product

Dot product

Cross product

Wedge product

Hadamard product

Voting ended onJan 5, 2024

[fair-lead]

if anyone has an understanding of the outer product. im having trouble with expanding u^v coordinate wise as shown here:

i know you just need the properties shown in the second image. but i cant figure out how to go from line 1 to line 2 using those properties (line 2 to line 3 i get tho)

[monaddecepticon]

man I'm gonna be so productive once I grok geometric algebra

My current understanding is:

Clifford algebras: vector spaces where some base vectors square to 1, 0 or -1

Something something tensor products

You can multiply any two multivectors by [checks notes] adding together two different products (how do I construct those? Why add them?)

Should I just sneak into a consultation at a local uni? LOL

[lady-inkyrius]

— My tags on that poll about people's favorite type of product

Geometric algebra¹ sort of scratches the same itch for me as something like category theory does I think. They're extremely general but can be nicely applied to various parts of computer science that I'm also interested in (mainly graphics programming and functional programming respectively²).

As someone who isn't studying maths formally and is mostly learning this stuff with the help of YouTube, how do people not actually doing a university course in it go about learning higher level maths? YouTube videos are all well and good but they can sometimes leave much to be desired.

I guess I could always just implement them in a program or something – like writing a ray tracer using geometric algebra instead of standard linear algebra and quaternions – but that has the problem of feeling like I'm learning a very specific form of the maths rather than the nice generality of the abstract form that attracted me to it in the first place, and that should probably be understood before concretising.

¹ Is it usually "geometric algebra" or "a geometric algebra"? I still haven't quite gotten used to the way "algebra" is used as a countable noun in parts of maths. Same with people saying stuff like "the lambda calculus" honestly, it just sounds wrong.

² Though in some ways geometric algebra reminds me of functional programming as well, the realisation of how separating out higher grade k-vectors rather than treating them as "pseudo-" works feels like understanding the power of a good type system. Though I will admit that it has made me slightly less confident that I could give an answer to the question "What is a scalar?"

[humormehorny]

Hey nerds! If you are a mathematician or a programmer you need to understand this.

This is Freya Holmer. She is a tech artist - who is interested in programming and mathematicsa programmer and mathematician.

This is from a talk called Why Can’t You Multiply Vectors https://youtu.be/htYh-Tq7ZBI

[art-of-mathematics]

No question from me rn, I just found out about geometric algebra and thought you’d find it really cool.

Thanks for letting me know! Sounds like a thrilling find! (will come back to it later)

(Source:)

Linear and Geometric Algebra (Geometric Algebra & Calculus, Band 1) : Macdonald PhD, Alan: Amazon.de: Bücher

[associahedron]

Geometric Algebra is a niche branch/spinoff of Linear Algebra (or a niche application of Clifford Algebras) that I happen to like. This video talks about how it can be used to write a 4D/nD physics engine.