The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #geometricproduct #multivectors Now that we know the properties of the geometric product, we can start using it for calculations. We build a 4-dimensional basis for Cl(2), the Clifford algebra for a 2D plane. We then create multivectors as linear combinations of these basis blades, and we find out how to multiply them in general. 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 0:00 Introduction & recap 1:16 4 different basis blades and their grades 4:47 The Pascal triangle 7:21 Multivectors are linear combinations of basis blades 8:54 Special case: the product of 2 vectors 9:57 How to multiply 2 arbitrary multivectors 13:18 Basis-dependent formulas 14:15 Next: the square of the basis bivector This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )