An Introduction to Hilbert Spaces

In this video, I introduce the Hilbert Space and describe its properties.

Questions? Let me know in the comments!

Prereqs: Previous video on vector spaces, knowledge of what real and rational numbers are.

[VishalGupta-lwdk]

Wow.... You made sense in a really elegant, simple to understand and standard way.., .. Pls make more such videos on Quantum mechanics

[whitehorse]

Thanks for trying. I still have no idea.

[LydellAaron]

Thank you. Very helpful in adding to understanding. Hilbert spaces are a countably dense vector space which has an inner product that can reduce the vectors to a scalar, obeys conjugate symmetry rules, and is positive definite.

[Asdun]

God bless you for this great explanation

[azimsofi]

wow, this is simpler than a normal textbook, yet complete. thank you!

[derek]

Thank you for this video, clears some things for me. I cannot read all the stuff in the book, i just can't go through it without getting distracted and bored.

[christheother]

This is helpful. Frustrating to listen to some physics talks where I start to get confused about three words in. Apparently mathematical spaces are not just abstractions anymore, they ARE reality.

[info-hub]

Amazing lecture sir only one of its kind. If have searched so much but all explanations were very difficult to understand. You are amazing

[leonardoribeirodesouza]

That's awesome. I like so much when you work in another spaces.

[crazyboii]

Nice Work! I am very grateful for this. I love your channel. Keep it up.

[DialecticRed]

:/ came here because I know hilbert spaces are important for understanding spinors which are an important part of quantum field theory. I don't have the technical knowledge to understand this one right now though - I'm just looking to get a general understanding of QFT and General Relativity so I can really understand the fundamental rift between them, but right now I'm through my first semester of AP Physics II so a lot of this is going above my head, although I did notice a couple of parallels with the mathematical concept of quaternions. I probably didn't get a lot out of this video b/c I'm viewing it somewhat out of context, and I'm sure what your doing is great because it seems like its helping lots of people, but unfortunately I'm just not yet at the point where I can truly understand and appreciate Hilbert Space.

[gillesbaumann]

really good video! Good structure and clearly explained!

[rogerganga]

Am I the only one who came here after Siraj Raval's "complicated Hilbert space"? :/

[joshuakyanaalampour]

Amazing resource you are! Thank you so very much!

[adamgm]

That feel when you enter a video with 1 question but leave with 46.

[fbulderin]

Please link to the previous video in the notes. I got here searching for fock space and the video starts by referring to vector space, which I know nothing about, so a link to they previous video would help.

[nikilragav]

Is this your actual handwriting? It's beautiful haha. What program do you use to write this in?

[moses]

Could you share the reference book you are using?

[abcdef]

so hilbert space is complete and has no gaps, can i say hilbert space is real number space? since as you said real number has no gaps and complete.

[ujjwal_]

is there a reason as to why hilbert spaces need to be complete and separable?