Geometric Algebra, First Course, Episode 09: Exterior Product Redux

We take a look at our incomplete exterior product implementation and complete it so that it can operate on all elements of the algebra. In doing so we see a description of the exterior product of any number of vectors in terms of the anti-symmetric combination of geometric products of those vectors.
The STEMCstudio project for this episode can be found at:

[hankdewit]

Hi David. Thank you for these videos. I've enjoyed going through them.

One question about the logic of the exterior product that we have defined here. I would have thought that the exterior product was the anti-symmetric part of the geometric product. The product of scalars is inherently commutative and so should be symmetric.

And by the definition, a ^ b = 1/2 (ab - ba), you would think would be zero for scalars, and a . b = 1/2 (ab + ab) would be 'ab', the symmetric part of the geometric product.

By this logic a ^ b = 0 [ so we should have checkEQ(one.ext(one), zero) ] for scalars, not a * b [ ie !checkEQ(one.ext(one), one) ]

[DMWatchesYoutube]

im new to this and i am not sure of the words to use, i am trying to implement a general algorithm to get the exterior product of any tensor which i plan to treat as a multivector,
i am doing something like this kroneckerProduct(b, transpose(a)) - kroneckerProduct(a, transpose(b)). I am wondering if i should get the determinant of this product, or if i am doing something wrong.

[ibgib]

Fantastic video. I'm reslly appreciating seeing your tables mapped to the function implementations. That is helping with getting used to the computational side 🧮🎉