“I highly recommend the video”
Made geometric algebra click in about 40 minutes
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I highly recommend the video this video linked from the site above ~40 minutes, and I get the point of geometric algebra now.
A Swift Introduction to Geometric Algebra
1.1M views · Aug 18, 2020 · 44:23 · 7 HN recommenders · 7 mentions · discussed 2020–2024
An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.
Why Hacker News points people here: HN calls it the best video on geometric algebra, one that makes the subject click in about 40 minutes.
“If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video”HN comment, 2022
What Hacker News said 7
“has the best video by far on Geometric Algebra (imho)”
Considered the best video on geometric algebra
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This little known channel: sudgylacmoe - which doesn't seem present in the list, has the best video by far on Geometric Algebra (imho) this video
“If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video”
Inspiring overview of the power of geometric algebra
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If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video "A Swift Introduction to Geometric Algebra" this video
“Here are 2 45mn videos you'll not regret”
Shows quaternions as simple multivectors in geometric algebra
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You should jump straight to geometric algebra. It's actually simple there. Quaternions and Complex Numbers are about just some not so special multivectors. Here are 2 45mn videos you'll not regret: link this video
“Some of the perceived complexity of complex numbers and quaternions seems to stem from not knowing the bigger picture.”
Gives the bigger picture behind quaternions and complex numbers
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Also check out this video and link Some of the perceived complexity of complex numbers and quaternions seems to stem from not knowing the bigger picture.
“Primer on the topic”
Primer on geometric algebra with eye-opening physics connections
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Note don't to be confused with Algebraic Geometry they are different; When I first came across this topic it was eye opening, especially the fact that you could squeeze Maxwell's equations into one and the fact that pseudovector create by cross product from physics is just a bivector which in 3d could be represented like a vector orthogonal to the plane created by the two vectors in the product Primer on the topic this video (And other videos on his channel) Another greate playlist is link BTW the author has the following page link with great infographics and references
“You're in for a nice trip, the concept is called Geometric Algebra”
Introduces geometric algebra, which generalizes cross products
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You're in for a nice trip, the concept is called Geometric Algebra: this video (~50m video) TLDW: Yes, the concept is there, makes much more sense than a cross product (which is just an oriented area) and generalizes really nicely. Alternatively, read: link