Seem reasonably concise, but I think Kreyzsig's Introduction to Functional Analysis with Applications fills the "gap" that this paper wants to fill. It's readable, has applications, exercises, and is more complete.
From my undergrad engineering math I understand some context here but am getting confused after a decade of programming. Words like "compact" and "closure" [0] probably do not translate directly to the mathematics space from software development - but don't really expect them to...
Thanks for the post it's a good kick in the rear to explore conceptually what eigenvalues/vectors are again!
Although it is about a specific application, optimization, it is a good book to get a sense of infinite dimensional vector spaces. I would also recommend Halmos. His book surreptitiously introduces you to that subset of linear algebraic notions that survive inti infinite dimensional spaces.
if you take the spectral theorem, for example, there is a direct connection between linear algebra and functional analysis, basically it's linear algebra in infinite dimensions
Genuine question: does the writing tool matter at all here if the exposition is clear and mathematically correct? I’ve seen great notes written in Word, LaTeX, and even slides—quality seems independent of format.
both no in principle, and when you're used to reading LaTeX, word is ugly. It's a milder form of how if these notes were handwritten it wouldn't matter, but it would also be less appealing than them being typeset well.
It's "bad form" to write STEM papers in Word. Which is stupid, of course, as every major publisher offers both Word and LaTeX templates. I wish they'd offer Typst too.
Thanks for the post it's a good kick in the rear to explore conceptually what eigenvalues/vectors are again!
[0]: from looking up "compact operator" https://en.wikipedia.org/wiki/Compact_operator
https://ia801706.us.archive.org/7/items/in.ernet.dli.2015.14...
Luenberger, Optimization By Vector Space Methods.
Although it is about a specific application, optimization, it is a good book to get a sense of infinite dimensional vector spaces. I would also recommend Halmos. His book surreptitiously introduces you to that subset of linear algebraic notions that survive inti infinite dimensional spaces.