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!

[0]: from looking up "compact operator" https://en.wikipedia.org/wiki/Compact_operator

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.

That sure is one compact document. Pun intended. The document is very readable too.

(2019). No exercises.

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.

Not LaTeX...