Thanks in advance for reading! Basically I'm in a class that focuses on the abstract linear algebra, LMME, singular value decomposition, linear signal representations, linear algebra, and LMMSE for Machine Learning. It's a masters class, and I have taken linear algebra in college but I realize now that my college did not touch on the more abstract concepts of linear algebra like cauchy sequences, inner products, the triangle inequality etc. I rented out the Gilbert Strang Linear Algebra and Linear Algebra done right. Both had some sections on inner products, which helped, but that's it. The Lema Youtube Videos elucidated what an inner product definition is but not within a Hilbert space (good 1 hour youtube series if anyone ends up finding this question).
Is there any other book that could have a more complete introduction to Hilbert Spaces, or the math in general for Machine Learning? Hopefully with derivations of the proofs and the technicalities required for a Hilbert space. My professor notes only say: Left to the student to derive so I'm pretty lost.
Best Answer
The most thorough (but accessible) introduction to Hilbert spaces that I've seen is that given by Chapter 3 of Kreyszig's Introductory Functional Analysis with Applications. I find that his style is similar to that of Strang, so I think that if you like one you should like the other.