The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #geometricproduct #multivectors #complexnumbers #complexconjugate A very simple calculation shows that the unit bivector has exactly the same properties as the imaginary unit i. This means that the complex numbers are very naturally part of geometric algebra! We finally understand what i really is (a 90 degree rotation), and what the geometric product does (it produces complex numbers). We even get a very clean interpretation of complex conjugation: it flips the angle of a rotation, by flipping the sign of the antisymmetric part of the 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 Introduction & recap 1:21 The unit bivector squares to -1 3:29 The unit bivector rotates vectors by 90 degrees 5:27 Objects also act as operations 6:55 The geometric product produces complex numbers 7:54 The even-graded sub-algebra 10:31 The complex conjugate flips the angle 14:50 Conclusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )