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A Swift Introduction to Geometric Algebra
A 44-minute talk by sudgylacmoe about algebra and geometry and relativity, on the Mathematics shelf. It came up in 2 Reddit threads, in r/3Blue1Brown and r/math. It is pitched at advanced level.
sudgylacmoe, Talk, 44 min, 2020, on the Mathematics shelf
This video is an introduction to geometric algebra, a severely underrated mathematical language that can be used to describe almost all of physics. This video was made as a presentation for my lab that I work in. While I had the people there foremost in my mind when making this, I realized that this might be useful to the general public, so I also tried to make this useful to others as well.
Study notes
Advanced, Lecture. Step 3 of 13 in The mathematics of change and signals
Helpful first
- Vectors
- Linear algebra
- Comfort with symbolic notation
What it builds
- Introduce bivectors and higher-dimensional primitives.
- Generalize the geometric product.
- Interpret multiplication as rotation.
Useful moments
- 4:32From scalars and vectors to bivectors
- 7:49K-vectors and the geometric product
- 18:54Multiplying a vector by i
Check yourself: What geometric information can a bivector represent that a scalar cannot?
Notes are based on metadata, Reddit context and selected English caption passages. They are not a review of every claim in the video.
