A Swift Introduction to Geometric Algebra

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. This video was made using manim a math animation library. Several things in this video were incorrectly simplified. Please watch the video before reading the rest of the description. Before I get into the things that were incorrectly simplified, I need to state a few definitions. The grade of a kvector is defined to be k. A blade is defined to be the outer product of vectors. A kblade is a blade of grade k. Some of the terminology between linear algebra and geometric algebra can be confusing, such as the use of the terms vector space and dimension. Because multivecto