Versors, rotors, and spinors | Geometric algebra episode 14

#geometricalgebra #quaternions #complexnumbers #versors #sandwichproduct #spinors The crusts of the sandwich product have many interesting properties. They are versors because they are very easy to invert. They are rotors because they produce rotations. And they are also spinors because they don't return to normal after you give them a full turn. 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 We have a long list of interesting resources for you today. Check them out if you want to learn more: [MTB 1]    • Let's remove Quaternions from every 3D Eng...   Rotors generalize complex numbers and quaternions to any dimensions. This video beautifully illustrates how rotations are performed in geometric algebra, and why rotors are more general than quaternions. [MOM 1]    • Geometric Algebra  - 3D Rotations and Rotors   Mathoma: rotors in higher dimensions. [MOM 2]    • Geometric Algebra - Rotors and Quaternions   Mathoma: rotors & quaternions. [MOM 3]    • Geometric Algebra - Linear Transformations...   Mathoma: The connection between rotors and orthogonal matrices. Rotors have a determinant of 1, which makes total sense because they don't change areas. [HEST 1] https://davidhestenes.net/geocalc/pdf... A good introduction to geometric algebra. Starting on page 11, you can find an exposition about rotors and how they work. [GLD 1] https://geometry.mrao.cam.ac.uk/wp-co... An excellent PDF about geometric algebra that you can download for free. Chapter 3 talks about spinors. [EIG 1]    • Spinors for Beginners 1: Introduction (Ove...   The ever amazing Eigenchris explains spinors in so much detail that your brain will start spinning inside your skull. 0:00 Introduction 0:37 What are versors? 3:55 How to construct operations, and how to apply them 4:52 Rotors are versors with an even number of unit vectors 6:47 Unit complex numbers are rotors 8:43 Unit quaternions are also rotors 9:37 Lie groups & Lie algebras 11:41 What are spinors? 14:10 SU(2) is a double cover over SO(3) 15:23 Rotated spinors pick up a minus sign 18:36 Conclusion This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )