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.
dieselgate 1 days ago [-]
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.
wolfi1 23 hours ago [-]
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
synapsehire 1 days ago [-]
[flagged]
oakinnagbe 1 days ago [-]
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.
throwaway81523 1 days ago [-]
I would say it's not statistically independent. See https://scottaaronson.blog/?p=304 item #1. So we get to add another exception, which is fine.
oakinnagbe 4 hours ago [-]
That feels more like a selection effect than a property of the writing tool itself.
1 days ago [-]
anioko1 1 days ago [-]
Interesting!
mswphd 1 days ago [-]
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.
oakinnagbe 4 hours ago [-]
[flagged]
hamburgererror 1 days ago [-]
Not LaTeX...
CyLith 1 days ago [-]
DABM writes everything in MS Word.
DarkNova6 1 days ago [-]
So... ?
maleldil 1 days ago [-]
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.
1 days ago [-]
Rendered at 17:52:19 GMT+0000 (Coordinated Universal Time) with Vercel.
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.