sudgylacmoe | Addendum to A Swift Introduction to Geometric Algebra @sudgylacmoe | Uploaded March 2022 | Updated October 2024, 1 hour ago.
This video is an addendum to my most popular video, A Swift Introduction to Geometric Algebra. It clears up some misunderstandings that have arisen from the original video, and then describes two useful ways of understanding the geometric product. This also leads to a discussion of the other flavors of geometric algebra, such as PGA and CGA.

If you want to learn geometric algebra at a much slower pace, check out my video series From Zero to Geo. Here's a link to the playlist for it: youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy

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Sections
00:00 Introduction
01:00 Common Misunderstandings
02:28 Understanding the Geometric Product
03:37 Product of Two Vectors
05:32 Product of Vector With Bivector
07:26 Product of Two Bivectors
09:18 Product of Two Multivectors
09:42 Other Flavors of Geometric Algebra
10:58 Revisiting the Geometric Product
12:43 Geometric Product in VGA
14:44 Problem With 3D Reflections
16:09 2D PGA
19:37 3D PGA
20:47 2D CGA
22:56 Conclusion