Today we continue our journey toward building up (discrete) exterior calculus by talking about how to measure little k-dimensional volumes. Just like rulers measure length, and cups measure volume, k-forms will be used to take measurements of the little k-dimensional volumes or k-vectors that we built up using exterior algebra in our previous lecture. Such measurements will ultimately allow us to talk about integration over curved spaces; in the discrete setting, these measurements will be the basic data we associate with the elements of mesh.
I just realized that the formula for determinant is just a special case of wedge product…
So simple yet all these years I have never known…
This is amazing
And why 3d cross product is using that ijk trick.