The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #wedgeproduct #pseudoscalar #pseudovector #hodgeduality #duality #crossproduct In 3 dimensions, we construct an 8-dimensional Clifford algebra. One uniquely aspect of this algebra is that each plane has exactly one associated normal vector. This creates confusion in physics, where rotations are often explained in terms of an axis of rotation, rather than a plane of rotation. This leads to the cross product, an abomination that should be replaced by a much better alternative: the wedge product. 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 Recap of 2D geometric algebra 1:55 3D geometric algebra 4:06 Confusion between vectors and bivectors 6:47 The strange definition of the cross product 8:26 Examples of the cross product in physics 10:31 The wedge product is much better than the cross product 12:08 Proving that the wedge & cross products are duals 13:28 Why the wedge product is better This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )