>>16635835
>Hilbert spaces and Cauchy-Schwarz inequality ain't basic algebra
They literally are. CS is one of the axioms of inner products; you cannot not know about it and claim you understand linear algebra in any capacity. Hilbert spaces are just inner product spaces with an additional requirement of completeness so you can do analysis on them. The usual R^n is a Hilbert space if you didn’t know.
>Fourier transforms are intermediate shit in comparison
Fourier transforms require you to be proficient in topology, measure theory, and functional analysis. It is an active area of research; we have no idea how to approach Fourier analysis on non-compact topological groups. There is only a certain class of such groups where we have a good idea of what’s going on based on pioneering work of Wigner and further tools developed by Mackey.

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Holy shit I just learned that Heisenberg uncertainty principle has nothing to with quantum mechanics and is just a consequence of wave properties and…