sudgylacmoe | An Overview of the Operations in Geometric Algebra @sudgylacmoe | Uploaded April 2023 | Updated October 2024, 4 hours ago.
This video is an overview of some of the basic operations in geometric algebra. It covers operations like the geometric, outer, regressive, and inner products, some of the involutions, and a few other operations. It also tries to describe these operations in a way that applies to arbitrary flavors of geometric algebra, to allow for a smoother transition into these other flavors.

In case you don't really know anything about geometric algebra, I would suggest watching my introduction to it first: youtube.com/watch?v=60z_hpEAtD8
I also have an important addendum that I made to that video as well: youtube.com/watch?v=0bOiy0HVMqA. This video assumes that you have a basic understanding of vanilla geometric algebra already, which you would get from these videos.

Discord: discord.gg/3Zj59zA2Rg

Patreon: patreon.com/sudgylacmoe

Patreon Supporters:
AxisAngles
Bill Six
Christoph Kovacs
David Johnston
LoganMP
p11
Richard Penner
Rosario

Sections:
00:00 Introduction
01:09 Multivectors
03:31 Grade Projection
04:50 Geometric Product
05:12 Geometric Understanding of the Geometric Product
06:40 Algebraic Understanding of the Geometric Product
10:01 Understanding the Geometric Product with Transformations
12:01 Reverse
14:21 Grade Involution
15:38 Magnitude
18:54 Outer Product
22:54 Regressive Product
26:51 Dual
30:33 Inner Product
39:49 Conclusion