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_alternator_ 20 hours ago [-]
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 19 hours 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 17 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 18 hours ago [-]
[flagged]
oakinnagbe 21 hours 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 21 hours 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.
20 hours ago [-]
anioko1 20 hours ago [-]
Interesting!
mswphd 18 hours 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.
hamburgererror 23 hours ago [-]
Not LaTeX...
CyLith 23 hours ago [-]
DABM writes everything in MS Word.
DarkNova6 23 hours ago [-]
So... ?
maleldil 18 hours 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.
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.