Vector division | Geometric algebra episode 1

#geometricalgebra #geometricproduct #dotproduct #wedgeproduct #crossproduct #complexnumbers We invent a new product for vectors. Under this geometric product, vectors have inverses, which allows us to calculate with them as if they were numbers. This opens up a vast world of cool techniques and concepts called geometric algebra. I am very grateful to Steven De Keninck for answering some of my technical questions. Specifically, he gave me a solid intuition for why the geometric product is defined the way it is. You can support us on Patreon, where you can already watch all the Geometric Algebra videos and get access to exclusive content. Unfortunately, we won't be publishing any new videos after Geometric Algebra, at least not in the near future. Your support is still more than welcome of course: https://www.patreon.com/user?u=86649007 Don't forget to check out these links: [BIV 1] https://bivector.net/ A website with many resources to get started with geometric algebra. This includes videos and articles, but also programming tools and cheat sheets. Definitely the best place to start learning. [SUDGY 1]    • A Swift Introduction to Geometric Algebra   One of the most popular introductions to geometric algebra. This gives you a good feel for the many connections and bridges to other topics. 0:00 Finding a good product for vectors 1:45 Why are vector inverses important? 3:08 Why do we need a brand new product? 5:06 The requirements for our new product 7:34 How do we make vectors invertible? This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )