Functional Analysis vs. Linear Algebra – The Infinite-Dimensional SHOCK
65K views · Aug 28, 2026 · People & Blogs
Comments · 73
@99fromscartch · 1 month ago
Excellent summary. Functional analysis is essentially the linear algebra of infinite-dimensional spaces. Highlighting the failure of the Heine-Borel property and the unbounded nature of differentiation correctly identifies the core challenges of modern analysis
18
@scollyer.tuition · 4 weeks ago
This is the first video that I've seen from your channel and I'm very impressed. You've managed to make your presentation interesting and have also allowed the viewer to see why they may want to learn some functional analysis by the nice comparisons to linear algebra, pointing out where it fails in the infinite dimensional case. There are many books that fail to do this, plunging into a topic with no motivation nor any sense of the historical development of the subject.
10
@SR-ml4dn · 5 days ago
Excellent presentation, I can't think of other explanations that are so good as yours.
1
@geraldkitaka3095 · 5 days ago
Thanks for your time, energy and knowledge.<br><br>Longlive
1
@yshkodama6231 · 3 weeks ago
この放送は、基礎レベルの線形代数だけ理解している者にも、関数解析の必要性を分かりやすく説明していると思う。素晴らしい。
4
@Erotemic · 2 weeks ago
this is connecting a lot of dots for me that I've loosely held but never formed the comprehensive picture. Thanks for building this lecture.
@jivansh6544 · 10 days ago
this is too good bro , a lot of thanks to teach these things to me , love you and waiting for other works in maths like this
@PlasmaFuzer · 1 month ago
Absolutely beautiful topic. The richness only increases with time.
5
@ralphschraven339 · 4 weeks ago
Absolutely mindblowing content. This really put together so many different pieces of linear algebra and (functional) analysis and how it relates to applications as well.
@AMADEOSAM · 4 weeks ago
Excellent explanation thanks …
3
@atlai9486 · 3 weeks ago
I hope you'll discuss spectra of operators and the notion of continuous spectra in future lectures because I'm still confused about these!
@madaaz6333 · 4 weeks ago
Great video! 🤩
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