Are 8850 Form Supplemental 2016-2023

So, I was reviewing some of the old lectures on forms and I realized I kind of glossed over something that can cause confusion if you start studying other books. So, I want to quickly go over the normalization of forms, and I think this would be best inserted right after lesson 27 of what is a tensor. Right after that lesson, maybe this quick lesson would best fit. But the issue is that forms can be normalized in a couple ways, and what lesson 27 offered up was the anti-symmetrization operator which 4p forms for rank p tensors, which I'll call KP. This all works for P vectors as well, but we'll just do it in terms of P tensors. The idea was that you could take any tensor and run it through the anti-symmetrization operator, which was writing 1 over P factorial multiplied by the sum over all permutations of the parity of the permutation multiplied by the Sigma transpose of the tensor T. We went through this in lesson 27 about what this exactly meant. The point is, I think I also demonstrated why this P factorial is in there, and the reason it's in there is because we want this to equal T when T starts anti-symmetric. So, what I want is K a P of T to equal T whenever it's always true that P transpose of T equals the Sigma transpose of T equals the parity of that transposition times T itself. When this is true for T, then this has to be true for the anti-symmetrized version of T. We went through that proof in lesson 27, but that explains the origin of this factorial, so that's a really important place to start. The other point I want to remind people of is...