Inner products and Hilbert spaces? More like "Interesting lectures and hearty specifics!" Thanks again for making all these incredible videos with such nice examples and clear explanations.
Hi, are you going to talk more about the case (c) C([0,1], IF) in the future videos? This case seems to be very important for many applications. Thanks!
Are Fourier series cauchy sequences in the continuous function space we defined? If so then the fact that Fourier transforms can approximate discontinuous functions to an arbitrary close degree is because the continuous functions aren't a Hilbert space
By "because" you meant "the cause"? As in, you provided an example of a Cauchy Sequence converging to a discontinuous function. So that would be "the cause" of continuous functions armed with the usual norm not being complete: we have Cauchy Sequences not converging to an element in the space of continuous functions.
@@brightsideofmaths Yes, if you watch it on your phone, it's just too bright, maybe it's just me, but it's hard to watch, which is ashame since it seems to be great content. Maybe you can do a questionnaire about it ? Anyway thanks for asking.
I cannot even stop watching your videos my friend lol. A very small suggestion and I am not sure if it would be too time-consuming. Some videos' subtitles are closed and some of them are wrong (e.g., you are speaking English but the only option for the subtitle is German -> English, and the recognition of German is apparently not accurate cuz you are saying English). Adding subtitles by yourself might be too labor-intensive but could you open the Auto-generate (English) for those missing ones? Thank you!
@@brightsideofmaths I see I see. I did not know TH-cam's subtitle policies lol. I will pay attention to that and let you know (or may request TH-cam to auto-generate some subtitles) in the future. Thank you!
I miss the quizzes and I also noted that you are start using complex numbers I haven't take the complex course yet do you believe that I could finish this one (I mean understanding properly) without taking that one before? O would be better to go for the complex one right now? Thanks
Complex numbers don't change so much. However, it is always good to know how they work. You can check my course about them, which is also short: tbsom.de/courses/start_learning_complex/overview/
At the beginning what does C^n mean ? I understand R^n, but C^n ... does it mean an n-D space where each dimension is a complex number? does it make sense ?!
Your videos are awesome. So well organized and so helpful. Plus you just seem friendly and kind, which goes a long way too. Thanks!!
Your videos are very nice and very easy to learn with.❤
Inner products and Hilbert spaces? More like "Interesting lectures and hearty specifics!" Thanks again for making all these incredible videos with such nice examples and clear explanations.
i wish i found your channel when i was doing my undergrad... it would have been sooooo helpful
Thank you so much!
Awesome! Really enjoying these videos
One of the important fundamental topics for machine learning
Thank you , really you are amazing teacher ❤️❤️❤️
Thank you for your support :)
Hi, are you going to talk more about the case (c) C([0,1], IF) in the future videos? This case seems to be very important for many applications. Thanks!
Hi! Yeah, I will do that :)
At around 1:00 , why is it the complex conjugate for x_i ? And what part of mathematics studies this?
Complex conjugate is needed such that sqrt() defined a norm. A nice application for this inner product might be quantum mechanics.
I love your content dude :D
Are Fourier series cauchy sequences in the continuous function space we defined? If so then the fact that Fourier transforms can approximate discontinuous functions to an arbitrary close degree is because the continuous functions aren't a Hilbert space
Very nice :)
By "because" you meant "the cause"? As in, you provided an example of a Cauchy Sequence converging to a discontinuous function. So that would be "the cause" of continuous functions armed with the usual norm not being complete: we have Cauchy Sequences not converging to an element in the space of continuous functions.
thank you!
You're welcome! :)
you have interesting content, but I have to wear sunglasses to watch it, maybe next summer I have a look.
Would you prefer a dark version of the video?
@@brightsideofmaths Yes, if you watch it on your phone, it's just too bright, maybe it's just me, but it's hard to watch, which is ashame since it seems to be great content. Maybe you can do a questionnaire about it ? Anyway thanks for asking.
You do you like the dark version of the videos now? th-cam.com/video/Yz-G8DTY2kU/w-d-xo.html
@@brightsideofmaths Wow definitely 👌 😎😎 thanks very much 👍
Thank you for the effort 👌
I cannot even stop watching your videos my friend lol. A very small suggestion and I am not sure if it would be too time-consuming. Some videos' subtitles are closed and some of them are wrong (e.g., you are speaking English but the only option for the subtitle is German -> English, and the recognition of German is apparently not accurate cuz you are saying English). Adding subtitles by yourself might be too labor-intensive but could you open the Auto-generate (English) for those missing ones? Thank you!
I am sorry but auto-generated subtitles is TH-cam's call. I don't have a saying there :(
But maybe you can tell me which videos have the problem. Then I will put subtitles to it!
@@brightsideofmaths I see I see. I did not know TH-cam's subtitle policies lol. I will pay attention to that and let you know (or may request TH-cam to auto-generate some subtitles) in the future. Thank you!
I miss the quizzes and I also noted that you are start using complex numbers I haven't take the complex course yet do you believe that I could finish this one (I mean understanding properly) without taking that one before? O would be better to go for the complex one right now? Thanks
Complex numbers don't change so much. However, it is always good to know how they work. You can check my course about them, which is also short: tbsom.de/courses/start_learning_complex/overview/
Ur videos are great. And lovey.
I am struggling to find the mathematics behind Dynamic Time Wrapping and video on it
Glad you like them!
what is the english font of your writing?
What about (c) ? I am looking for proof .thank you
At the beginning what does C^n mean ? I understand R^n, but C^n ... does it mean an n-D space where each dimension is a complex number? does it make sense ?!
Yes, exactly :)
@@brightsideofmaths Amazing! I did not know such generalization of complex domain is possible! In which field such a generalization finds application?