Cauchy Schwarz Proof

This is one of my favorite math proofs! Usually the Cauchy-Schwarz inequality is proven using projections, but this proof is completely elementary. It is taken from Pugh's Real Mathematical Analysis-book. But beware it doesn't work for complex inner product spaces. Bon appétit! :)

Note: I forgot to mention: If a = 0, then v = 0, but then the statement is trivial.

[shaunderoza]

The one dislike must from someone who saw the words "discriminant" and "inequality" and got offended.

[cipicm]

even after 5 years this video is a masterpiece regarding the clearness of this proof. with no english background in mathematics it was still so easy to understand. thank you a lot.

[MarkJay]

"What is love?"

-Dr. Peyam

[duckymomo]

In France, it’s called Cauchy inequality
In Germany, it’s Schwarz inequality
In Russia, it’s just inequality

😂 LOL

[jamesclerkmaxwell]

"it's better than watching TV " 😂 I love you Prof. Tough crowd

[letladisebesho]

This is an excellent, clear proof. Now I finally get it. Thank you 🙏🏽

[afifakimih]

I'm a regular viewer of Dr. Peyam...his derivation methods are always unique.!!

[RealEverythingComputers]

At 1:40 when you show the summation of the dot product, do you mean i in superscript or subscript because its done in superscript in the video which confuses me with an exponent. Your clarification will be much appreciated. thx

[mokouf]

The camera man is actually blackpenredpen!

[rubentuquerrez]

I'v neve liked the proyections proof, but I love this one. I discover this by myself while I was studying for an exam. This was awesome. Thanks for the video Dr Peyam!

[vukstojiljkovic]

I love this proof dude! I was confused with the proof that they presented to me on the university, but this one, i love it. Keep making math videos, maybe i will join you in the near future! <3

[tlhomotsemoteme]

I am writing in 5 hrs and I needed you to boost my confidence. Thank you.

[randywilton]

This is an amazing proof! Way easier to understand than the one my real analysis prof gave us. Thank you

[chessislife]

Wow!! You get so many people that have same interest and passion as you, so fortunate

Love when he's writing on the board.
*hitmarker*
*hitmarker*
*hitmarker*

[josephinell]

Such an elegant proof! Thank you for sharing.

[abratumwe]

07:08 I didn't understand that part, we also have quadratic curves with positive answers only 🤔😕
What if the polynomial of t is only positive?

[bluemonk]

I don't understand why the proof suddenly decides to look towards the discriminant. It makes sense to use it since it guarantees that b^2 - 4ac <= 0 and thus b^2 <= 4ac (which is what we need), but how they decided to get there 🤷‍♂

[pheasant]

Very elegant proof. Easy to understand. Thank you!

[lamequemaciel]

Hey, professor! I was search the proof of Schwarz inequality for the context of Quantum Mechanics, mean that we can to use the complex space. But, I appreciate your proof.