Function Orthogonality Explained

[@TeamNolex]

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. :)

[@jonniburla9815]

Brilliant intuition to try to imagine what an Hilbert space is! Thank you

[@JordanEdmundsEECS]

I stole it from our good friends at MIT :)

[@Katutowavicle]

which MIT course ?​@@JordanEdmundsEECS

[@bhartitakshak3856]

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

[@JordanEdmundsEECS]

Thanks from the US :)

[@PixelContrast]

Never heard of any of this before, but you made my digital communication system study work a lot easier with this.

[@sidimohamedbenelmalih7133]

Thanks, that explains the whole idea of orthogonality

[@0hstar]

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 :)

[@mohitpandey4655]

Eigen value 👍

[@ganeshveilu380]

)llll*

[@MrChaluliss]

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!

[@user-cl3bl3lw6x]

really acurate explanation ! good job .. thank you , really helpfull video !

[@vector8310]

If you only knew how utterly grateful I am for this video. You've performed a public service.

[@ren7068]

omg thank you so so much!! this makes so much more sense now!

[@adelali2541]

SOOOOO well explained!!! Thanks Jordan!

[@HarshitSharma-qo1ws]

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♥♥♥

[@delourhossainpranto5856]

Thanks for also adding the applications.

[@laurastenhouse5949]

Brilliantly explained, thank you so much!

[@ahmetozbekler]

Very clear and the best explanation. Thank you.

[@wiggiesmallsaka9011]

great video, my man!

[@florentinosanchez3969]

Great video, thank you so for making it

[@lukemateo9500]

This was exactly what I needed thank you

[@chels_ktbffh92]

Beautifully explained! Thank you

[@gbolagadeolajide8595]

Excellent video!

[@_eagleofsuger_4631]

sincere thanks for your time

[@noornazeer4878]

this is perfect, thank you!

[@ryanchow4814]

This is GOD level information for my partial differential equation class

[@sergiolucas38]

the worse thing about this video is that it ends :( great video :)

[@aliabbas1572]

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

[@alewarten]

The best explanation! Thank you! Do you have anything on Fourier transform?

[@anuraggupta7969]

Great explanation. Loved the video !!!

[@alijohnnaqvi6383]

beautiful explanation. Really inspired. Thank you sir

[@marlonjareck7367]

this was great, thanks

[@NostraquedeoTX]

Beautifully explained. TY.

[@sau002]

Good one. should have more upvotes.

[@Milena-lg4dn]

This was incredibly helpful. Thank you!

[@peterjuma34]

you just made me understand orthgonaity

[@odedgilad9761]

thank you very much !!!!

[@user-gn8mf8on2v]

really helped me
thanks a lot

[@JordanEdmundsEECS]

Welcome!

[@hamedfarahani4281]

Amazing, thanks

[@hastythegent4706]

thank you so much, that was a very good explanation

[@CHEESYhairyGASH]

This really helped, thank you.

[@user-hv9rt7ye6h]

Very good explanation, thank you a lot

[@munabensaed2061]

This is Definitely useful

[@ignatiusebo-quansah3996]

well elaborated

[@ninjaman7123]

Such a good video thank you so much!

[@alilelo2524]

thank you

[@armpit1648]

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?

[@JordanEdmundsEECS]

Yup, that's the (real) mathematical formalism behind this video. Such a space, when used for functions, is called a Hilbert Space.

[@armpit1648]

@@JordanEdmundsEECS Thank you. I've seen the term Hilbert Space before and probably even read about it but didn't make the connection

[@user-rb2ss8vd9p]

Sir why orthogonality required

[@tomcat193]

What a great explanation. Thanks

[@abbasbookwala]

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

[@lucam9668]

he maybe mistakenly used x instead of π, but you get the idea

[@xXDarQXx]

yeah, I was wandering about that too, like do we just accept their function dot product is actually scaled by dx?

[@alntruisrtbredford]

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?

[@alxomnm]

outstanding explanation! thank you:)

[@akanchhakumari5666]

very beatiful video sir........

[@ankursingh1912]

THANKS SIR

[@Agogogogogogkglgkfndjesk]

Thank you very much.

[@marilu0007]

very nice, thank you!

[@mathmath3021]

There's a book about it?

[@soumyadip112]

Thank you❤

[@user-uj1vs8ng2r]

Great🔥

[@aponapon2073]

Thank you so much sir , I am grateful to you 😊😊

[@darinnozina2721]

but all the values are positive?? 7:58

[@mishazujev31415]

negative values come between x=pi and x=2pi

[@HuehuehueWolooo]

Explained - but really.

[@abdulhakimlukwago88]

please talk louder

[@peterjuma34]

thank you