Spinors for Beginners 12: How the Spin Group Generalizes Quaternions to any Dimension
Full spinors playlist: • Spinors for Beginners Leave me a tip: https://ko-fi.com/eigenchris Powerpoint slide files + Exercise answers: https://github.com/eigenchris/MathNot... 0:00 - Introduction 2:45 - Terminology overview 4:00 - Reflections in 3D space 9:00 - Reflections in 4D spacetime 13:20 - Rotations in 3D space 22:07- Exponentials 26:37 - Rotations + Boosts in 4D spacetime 32:07 - Galilean Boosts 32:42 - Spin(n) Groups 40:27 - Grade Involution 42:07 - Spin(p,q) Groups 44:15 - Transforming Multi-vectors 46:34 - Hestenes Definition of "spinor"
▶︎
Spinors for Beginners 13: Ideals and Projectors (Idempotents)
![Spinors for Beginners 10: SU(2) double covers SO(3) [ SL(2,C) double covers SO+(1,3) ]](https://i.ytimg.com/vi/Ay482u6b3Xo/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLDyyUjMF-ezT5djnNBg_hw-meJvPg)
▶︎
Spinors for Beginners 10: SU(2) double covers SO(3) [ SL(2,C) double covers SO+(1,3) ]
▶︎
One Formula That Demystifies 3D Graphics
▶︎
Fantastic Quaternions - Numberphile
▶︎
Dirac's belt trick, Topology, and Spin ½ particles
▶︎
The 248 Dimensional Object That Unifies the Universe
▶︎
Spinors for Beginners 11: What is a Clifford Algebra? (and Geometric, Grassmann, Exterior Algebras)
▶︎
Spinors for Beginners 16: Lie Groups and Lie Algebras
▶︎
The most beautiful formula not enough people understand
▶︎
I finally understood why the universe needs imaginary numbers (My mind is blown!)
▶︎
Spinors for Beginners 6: Pauli Vectors and Pauli Matrices
▶︎
Best Explanation of Gradient, Divergence and Curl
▶︎
3D Rotations in General: Rodrigues Rotation Formula and Quaternion Exponentials
▶︎
The Simplest Ancient Math Problem No One Could Solve
▶︎
How quaternions produce 3D rotation
▶︎
Why Science Doesn’t Make Laws Anymore
▶︎
Spinors for Beginners 15: Nilpotents, Fermions, and Maximally Isotropic Subspaces
▶︎
Spinors for Beginners 20: Lorentz Group / Algebra Representation Theory
▶︎
Visualizing the 4d numbers Quaternions
▶︎