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. :)

[jonniburla]

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

[tiagoandradedeoliveira]

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

[bhartitakshak]

I was fed up with this topic for a week only your one video made the topic crystal clear to me...Thank you so much, from India

[PixelContrast]

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

[sidimohamedbenelmalih]

Thanks, that explains the whole idea of orthogonality

[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!

[hstar]

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 :)

[vector]

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

[delourhossainpranto]

Thanks for also adding the applications.

[ren]

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

[HarshitSharma-qows]

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♥♥♥

[ΓιαννηςΜποτας-λλ]

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

[florentinosanchez]

Great video, thank you so for making it

[laurastenhouse]

Brilliantly explained, thank you so much!

[ahmetozbekler]

Very clear and the best explanation. Thank you.

[ryanchow]

This is GOD level information for my partial differential equation class

[lukemateo]

This was exactly what I needed thank you

[alewarten]

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

[sergiolucas]

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