Function Orthogonality Explained

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In this video I explain what it means for two functions to be 'orthogonal', and how we test for this orthogonality. This is actually an absurdly useful property that allows us to greatly simplify the Schrodinger Equation before trying to solve anything. I would argue it is one of the most fundamental mathematical properties of functions (at least of use to engineers and physicists), and underlies things like the Taylor Series and Fourier Transforms.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[@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.

[@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!

[@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*

[@tiagoandradedeoliveira8703]

Excellent explanation, thank you! I was studying numerical methods when I tripped over this topic.

[@sidimohamedbenelmalih7133]

Thanks, that explains the whole idea of orthogonality

[@adelali2541]

SOOOOO well explained!!! Thanks Jordan!

[@ren7068]

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

[@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♥♥♥

[@laurastenhouse5949]

Brilliantly explained, thank you so much!

[@delourhossainpranto5856]

Thanks for also adding the applications.

[@ΓιαννηςΜποτας-λ3λ]

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

[@lukemateo9500]

This was exactly what I needed thank you

[@vector8310]

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

[@alewarten]

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

[@ahmetozbekler]

Very clear and the best explanation. Thank you.

[@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

[@anuraggupta7969]

Great explanation. Loved the video !!!

[@ryanchow4814]

This is GOD level information for my partial differential equation class

[@_eagleofsuger_4631]

sincere thanks for your time

[@wiggiesmallsaka9011]

great video, my man!

[@Milena-lg4dn]

This was incredibly helpful. Thank you!

[@florentinosanchez3969]

Great video, thank you so for making it

[@alijohnnaqvi6383]

beautiful explanation. Really inspired. Thank you sir

[@peterjuma34]

you just made me understand orthgonaity

[@sau002]

Good one. should have more upvotes.

[@gbolagadeolajide8595]

Excellent video!

[@NostraquedeoTX]

Beautifully explained. TY.

[@hastythegent4706]

thank you so much, that was a very good explanation

[@CHEESYhairyGASH]

This really helped, thank you.

[@noornazeer4878]

this is perfect, thank you!

[@ninjaman7123]

Such a good video thank you so much!

[@alxomnm]

outstanding explanation! thank you:)

[@tomcat193]

What a great explanation. Thanks

[@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?

[@KALSHETTIKASHIRAJVITTHALNITGoa]

Sir why orthogonality required

[@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

[@marlonjareck7367]

this was great, 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?

[@munabensaed2061]

This is Definitely useful

[@ignatiusebo-quansah3996]

well elaborated

[@hamedfarahani4281]

Amazing, thanks

[@أروىعلاء-م6و]

really helped me thanks a lot

[@JordanEdmundsEECS]

Welcome!

[@odedgilad9761]

thank you very much !!!!

[@marilu0007]

very nice, thank you!

[@alilelo2524]

thank you

[@Agogogogogogkglgkfndjesk]

Thank you very much.

[@akanchhakumari5666]

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

[@soumyadip112]

Thank you❤

[@mathmath3021]

There's a book about it?

[@ankursingh1912]

THANKS SIR

[@يوسفالبطراوي-ث5ق]

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

[@chels_ktbffh92]

Beautifully explained! Thank you

[@Антонаа-л9в]

Very good explanation, thank you a lot

[@peterjuma34]

thank you