Thank you! I’ve always wondered where the integral comes from but thanks to your very simple, and honestly much better explanation, I‘m now slowly piecing the whole picture together. :)
I was fed up with this topic for a week .......But only your one video made the topic crystal clear to me...Thank you so much, sir.....Respect from India
This is really good! To help understanding this subject even better, I highly recommend the last video of 3blue1brown Linear Algebra's series, it shows how fuctions are actually vectors, really nice! good studies everybody :)
I am taking linear algebra right now and had intutions about this but wasn't sure. This video was helpful in clearing things up for me and I appreciate the stepwise reasoning a lot towards the end of clarifying!
Hi Jordan, Very nice explanation on the functional orthogonality. I am working on Zernike Polynomials for optical aberrations, do you have any suggestions to understand them in a much simpler way? or what the functional orthogonality on a unit circle means? Thank you in advance
It would have been nice if it was elaborated on how dx comes into picture while multiplying two functions and full transition from Sigma to Integration
I can't understand transition from sum to integral. Dot product for infinite vector is Σsin(x)*sin(2x) but not the Σsin(x)*sin(2x)*Δx How did you do this?
Thank you! I’ve always wondered where the integral comes from but thanks to your very simple, and honestly much better explanation, I‘m now slowly piecing the whole picture together. :)
Brilliant intuition to try to imagine what an Hilbert space is! Thank you
I stole it from our good friends at MIT :)
which MIT course ?@@JordanEdmundsEECS
I was fed up with this topic for a week .......But only your one video made the topic crystal clear to me...Thank you so much, sir.....Respect from India
Thanks from the US :)
Never heard of any of this before, but you made my digital communication system study work a lot easier with this.
Thanks, that explains the whole idea of orthogonality
This is really good! To help understanding this subject even better, I highly recommend the last video of 3blue1brown Linear Algebra's series, it shows how fuctions are actually vectors, really nice! good studies everybody :)
Eigen value 👍
)llll*
I am taking linear algebra right now and had intutions about this but wasn't sure. This video was helpful in clearing things up for me and I appreciate the stepwise reasoning a lot towards the end of clarifying!
really acurate explanation ! good job .. thank you , really helpfull video !
If you only knew how utterly grateful I am for this video. You've performed a public service.
omg thank you so so much!! this makes so much more sense now!
SOOOOO well explained!!! Thanks Jordan!
thank you so much man i was really confused in orthogonality of two signal like why we use integration there
but now it is clear♥♥♥
Thanks for also adding the applications.
Brilliantly explained, thank you so much!
Very clear and the best explanation. Thank you.
great video, my man!
Great video, thank you so for making it
This was exactly what I needed thank you
Beautifully explained! Thank you
Excellent video!
sincere thanks for your time
this is perfect, thank you!
This is GOD level information for my partial differential equation class
the worse thing about this video is that it ends :( great video :)
Hi Jordan, Very nice explanation on the functional orthogonality. I am working on Zernike Polynomials for optical aberrations, do you have any suggestions to understand them in a much simpler way? or what the functional orthogonality on a unit circle means? Thank you in advance
The best explanation! Thank you! Do you have anything on Fourier transform?
Great explanation. Loved the video !!!
beautiful explanation. Really inspired. Thank you sir
this was great, thanks
Beautifully explained. TY.
Good one. should have more upvotes.
This was incredibly helpful. Thank you!
you just made me understand orthgonaity
thank you very much !!!!
really helped me
thanks a lot
Welcome!
Amazing, thanks
thank you so much, that was a very good explanation
This really helped, thank you.
Very good explanation, thank you a lot
This is Definitely useful
well elaborated
Such a good video thank you so much!
thank you
So do we pretend they are two basis vectors in an N-dimensional space? Then there can be N orthogonal functions aka N basis vectors in such a space?
Yup, that's the (real) mathematical formalism behind this video. Such a space, when used for functions, is called a Hilbert Space.
@@JordanEdmundsEECS Thank you. I've seen the term Hilbert Space before and probably even read about it but didn't make the connection
Sir why orthogonality required
What a great explanation. Thanks
It would have been nice if it was elaborated on how dx comes into picture while multiplying two functions and full transition from Sigma to Integration
he maybe mistakenly used x instead of π, but you get the idea
yeah, I was wandering about that too, like do we just accept their function dot product is actually scaled by dx?
I can't understand transition from sum to integral. Dot product for infinite vector is
Σsin(x)*sin(2x)
but not the
Σsin(x)*sin(2x)*Δx
How did you do this?
outstanding explanation! thank you:)
very beatiful video sir........
THANKS SIR
Thank you very much.
very nice, thank you!
There's a book about it?
Thank you❤
Great🔥
Thank you so much sir , I am grateful to you 😊😊
but all the values are positive?? 7:58
negative values come between x=pi and x=2pi
Explained - but really.
please talk louder
thank you