sudgylacmoe - A Swift Introduction to Geometric Algebra

This week, I’m suggesting this video by sudgylacmoa.

This has been so useful to me, it really helped shape my intuition about the cross product. The identification between pseudo-vectors and vectors makes so much sense, and for me it really illustrates why, in finite elements, the magnetic field needs face (or Raviart–Thomas) elements which are basically bivectors—just like the magnetic field!

Also, this can be used to interpret the determinant as (crudely) the volume of the image, with \( f(e_1 \wedge … \wedge e_n) = f(e_1) \wedge … \wedge f(e_n) \) and \( {\rm det}(f) = \frac{f(e_1 \wedge … \wedge e_n)}{e_1 \wedge … \wedge e_n} \), which is just lovely.