Hilbert Space - Basic Introduction Part 2/2

[vesperala]

About the joke... I am not sure if I hear well.

Did you said "what are you doing in her space"? if yes, then maybe you should say "what are you doing in his space"...

Is it?

Of course it could be a girl mathematician and her boyfriend, but is useless to tell you about this symmetry property of your joke. :)

[cesarjom]

this is a poor explaination of what is a Hilbert Space. You randomly touched on some basic definitions of orthogonal and normal n-vectors, but never really explained waht are the basic properties (axioms) that define a H-space. Nor did you explain ideas of basis elements which is key to generalizing more infinte-dim vectore spaces

[shaharhada]

What the definition of Hilbert Space?

[bhigr]

I think you explained it very well. Hilbert space is simply any vector space, which has an inner product and a norm defined. A norm is a measure for distances between vectors. Finally any series of vectors that come arbitrarily close to each other (fourier series) must converge against an element in the vector space. That's important if you want to do any infinitesimal calculus in the vector space.

[bhigr]

@bhigr oh, not fourier, the other guy, cauchy series. Now every converging series is a cauchy series, but there are cauchy series that do not converge. The simplest series is 1/n in the space of positive non zero numbers. It doesn't converge because zero is not part of the space, but it is a cauchy series because the distance between the elements becomes arbitrarily close. If any cauchy series converges in a vector space, the vector space is complete.

[netmazter]

hey ....this was very helpful... could you also suggest come basic books to further my understanding on the topic... I am completely new to it.... thanks...

[hypodynamia]

hahahahaa .... the joke of the funny space of the hilbert space is abstract and so abstractedly funny. hahahaha ...

it's a funny space within the hilbert space which is abstract. hahahaha ... u get the joke? hahahahaha

[hypodynamia]

the joke is the funny space is the hilbert space which is abstract and made complicated to be funny. hahahaha .....

[hypodynamia]

The joke in the abstract space is a joke of a funny abstract space. hahahahahaha ....

very funny. You understand my joke? The funny hilbert space? hahahahahaha ...



[Arlesterc]

I don't understand the convergence of the sequence part and how it relates to the lines you drew. What is converging? Any sequence x1, x2, x3, x4.. to some point? Or all point sequences such as x1,x2,x3,x4... and y1, y2,y3,y4... to some common point.

[jhm155]

I'm still not so sure I understand. If all of our space (according to the joke) is in Hilbert space, then what would be an example of a space that would NOT be a Hilbert space?

Anyway, thanks for the lecture, I'm still trying to learn. This was more helpful than the Wikipedia page.

[miprabasiva]

I realize i was more physics oriented and I should have taken more mathematical view in explaining it. Hilbert space is an abstract math of all abstract math.

[allensugar]

@jhm155 people (in this case the girl) tend to think of space as Euclidean but they are mistaken since it's just an idealised special case of hilbert space. The joke is on the girl who is ignorant to this. Pretty dry but that's what mathematicians gotta do to get their fill.

Praba nice video-I agree with other people who find the lack of quality an issue but I do not have any problems with your accent.

[joelmartens]

I didn't get taught dot product until university :(

[666osiris666]

thanks was helpful

[fltnkim]

Thanks a lot,

It was very helpful video clip to remind the definition of Hilbert Space.

[pinkunath]

this lecture helps me a lot,

thanx

[pitagora11]

it will also be nice to discuss why completness of the space is important by examples of (pre)hilbert spaces which are not Hilbert. also you need to improve the presentation a little bit. which means consistence between examples and definitions, etc. it is clear that you know the stuff and you have the correct intuition and mostly a "physics" point of view of the subject. from a math perspective however probably a more rigouros presentation will help. overall good job and keep them coming!

[miprabasiva]

Dear Pitagora11,

Thank you for the feedback and I will make the necessary fine tuning to my future video lecturers.

TY, - Praba

[pitagora11]

" ortho"  is not a "fancy" word . is just the greek(the first ones which consistently studied those things) term for perpedicular.

[sadhusuman]

Keep going....that was really useful

[s3107328]

at 7:28 "...all finite dimensional space are instances of hilbert space".. ???

But your definition stated that Hilbert space is infinite dimensional... I think you know what your talking about, but you have to clear up your delivery.

[miprabasiva]

All finite dimensional space are sub space of infinite dimensional space.. I see your point, I was not mathematically precise in my description. Thank you for the feedback. I will make the necessary fine tuning in the future lecture.

[FarFromEquilibrium]

All the encouragement you need right here bro! I'd love to see a breakdown of Heisenbergs and Schroedingers and how Heisen's starts with classical and quantum falls out of it. Saw an MIT lecture from Itunes U with prof Donald Sadoway where he spoke fo it like that. I also have some curiosities about QFT and QCD but the LAgrangian is so beyond me Im not sure how well Id follow it.

Anyway thanks again.

[FarFromEquilibrium]

this is great. keep them coming :D

[miprabasiva]

Dear FarFromEquilibrium,

Thank you for your encouragement and kind words. I will try to post more..

Thank you - Praba