The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #geometricproduct #dotproduct #wedgeproduct #crossproduct #complexnumbers We derive the formula for the geometric product of two vectors. Using the simple rules for the product, we simplify the formula to a sum of a scalar part and a bivector part. We also hint at the connection with complex numbers. 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 [MOM 1] https://www.youtube.com/watch?v=RbKjaPDoGlw&list=PLpzmRsG7u_gqaTo_vEseQ7U8KFvtiJY4K&index=11 This video explains how to calculate the geometric product between multivectors more generally. 0:00 Introduction 0:47 The geometric product of 2 vectors 3:48 The pairwise products between basis vectors 4:56 Dot product & wedge product 6:31 Can we add different kinds of objects together? 8:06 Scalar part & bivector part 8:54 Orthogonal & parallel 12:30 Conclusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )