How is 4) supposed to imply 3), I don't get it

>>8583529
3 follows right from the definition of the hilbertspace norm from the scalar product.
4 is some obscure result in linear algebra, which probably can't be generalized to an infinite dimensional hilbert space setting

>>8583529
Look at the case that A is just a 1 x k vector. Then you could consider [math]\mathrm{det}(A^\top A)[math] something like [math]\langle A, A \rangle = |A|^2[/math]. The minors of that vetor are also just numbers then, so the determinants are just the numbers themselves again, so it kind of says something like [math]|A|^2 = A_1^2 + \dots + A_k^2[/math]. You could consider the equation some kind of a generalization of that, but then again not really, as I don't believe [math]\mathrm{det}(A^\top A)[/math] is a proper norm.

>>8583553
I found it on funnyjunk, which made me happy the hoi polloi would care about what a hilbert space is, but someone suggested that 3) implied 4) and that they should be switched
So I'm not sure.

>>8583537
I get the same vibe from it..

>>8583529
https://arxiv.org/pdf/1001.0201.pdf

>>8584886
>I think the theorem might be of pedagogical interest
dropped