The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #wedgeproduct #linearalgebra #matrices #determinant #cramersrule Linear algebra is a huge set of tools for manipulating vectors and solving systems of equations. Today we find out that we can replace many of those tools with the humble wedge product. It automatically gives us the correct formula for the determinant of a matrix. It also helps us solve equations, and explains where Cramer's rule comes from. 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 Here are some very interesting links that allow you to continue learning: [MOM 1] https://www.youtube.com/watch?v=dnzUgDl43rQ An excellent video that shows you how to solve a system of linear equations using the wedge product. You can estimate the result by looking at the lengths and areas of the geometric objects involved. [TN 1] https://www.youtube.com/watch?v=sJmSOKKpqZc Timothy Nguyen talks about determinants, orientation, and the wedge product. [AMD 1] https://www.youtube.com/watch?v=0VGMxSUDBH8 Alan Macdonald gives a good overview of some applications of geometric algebra in linear algebra, including determinants. 0:00 Introduction 1:04 Determinants in geometric algebra 6:11 The norms of blades are determinants 8:45 Linear independence 10:31 Solving systems of linear equations using the wedge product 14:00 Conclusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )