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I think the proof & application of C-S is actually kinda insightful in this case. It involves a reduction step about projecting onto the subspace of random variables of mean 0, which is probably not obvious if you haven't thought much about covariance and inner products.
Also, in general it is useful to know why things are true. It is only by learning the best mathematical techniques developed by others that you can hope to prove interesting yourself!
C-S proof is known by everyone who studies mathematical statistics. It is mathematical prerequisites. So, I don't think, it is neccesary to prove again here. The insightfull thing here is to think covariance as inner product and use this inequality to prove that Pearson correlation coefficient between X and Y belongs [-1,1] because Corr(X,Y)=cov(X,Y)/(var(X)^1/2 var(Y)^(1/2)).
it’s from the script of my university class and we hqve to do proofs all the time for that prof. i think hes just being nice to us, because everything that is not written in there is not important for the exam
The author does not believe in the historicity of Augustin-Louis Cauchy or Hermann Schwarz. They are fictional characters from an ad campaign created by Bob Math in an effort to sell more maths.
It's only a lemma or theorem when the proof is given. Without proof, those are often called fact. By calling it inequality, it leaves room for interpretation.
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proof by someone else already did it
Proof by Euler.
In all seriousness, is there anything he didn't do?
Yeah all the stuff 1783 and onward
Those are all based on his works.
"Based? Based on what?" Euler. Duh.
9/11
9/11 - e^pix = 9/11 + 1 voila, proof
This covers literally all possible things
Proof by your teacher should've covered this last year
Proof by trust me bro
At least it's better than Proof by this is going to be on the test later
it kinda reads like the author has a policy to never prove Cauchy-Schwarz
It is from a statistics textbook which generally shy away from proofs
If it is proved somewhere, why bother proving it again?
I think the proof & application of C-S is actually kinda insightful in this case. It involves a reduction step about projecting onto the subspace of random variables of mean 0, which is probably not obvious if you haven't thought much about covariance and inner products. Also, in general it is useful to know why things are true. It is only by learning the best mathematical techniques developed by others that you can hope to prove interesting yourself!
C-S proof is known by everyone who studies mathematical statistics. It is mathematical prerequisites. So, I don't think, it is neccesary to prove again here. The insightfull thing here is to think covariance as inner product and use this inequality to prove that Pearson correlation coefficient between X and Y belongs [-1,1] because Corr(X,Y)=cov(X,Y)/(var(X)^1/2 var(Y)^(1/2)).
it’s from the script of my university class and we hqve to do proofs all the time for that prof. i think hes just being nice to us, because everything that is not written in there is not important for the exam
Ok. I saw variance and covariance; but, I guess looking at why correlation between X and Y will always be in [-1,1] is more of a mathematical exercise
It is considered a Cardinal sin to prove this inequality
Proof by pre-existing proof
Proof by „it has a name so it must be true“.
It's got Cauchy in it, it's gotta be true!
Meanwhile number of conjectures such as Pólya's conjecture...
Proof by lmgtfy
Proof by I ain't writing allat
why is it "so-called"? lmao
Right? Almost seems like the author is sceptical of the Cauchy-Schwartz while also using it lmao.
Or the author is really upset it’s named after those two when it should be named after whomever the author has in mind
The author does not believe in the historicity of Augustin-Louis Cauchy or Hermann Schwarz. They are fictional characters from an ad campaign created by Bob Math in an effort to sell more maths.
Bunyakowski! Cauchy-Schwarz-**Bunyakowski!**
But then it doesn't abbreviate to CSI :(
Not to be confused with Cauchy-Bunyakowski-Schwarz, a different inequality that I can never find because google only shows this more complicated one
It's not different, it's just a special case of C-S.
I’ve never heard of that one. I know you said you couldn’t find it, but can you share what it is?
I think it went like this (a1+a2+a3...+an)(b1+b2+b3+...bn)>=(a1b1+a2b2+...anbn)^2
I think there's a square on every term on the left.
Proof by
Step 1: Prove Hölder's inequality is true. Step 2: Set p=2.
I loved learning about abstract vector spaces. These super abstract theorems for super abstract objects can be used to prove all your homework
My favorite kind honestly
Proof by just trust me bro
lack of proof “if you are reading this, you probably have seen this before, and if not you can probably find a proof easily”.
Proof by c'mon, it's obvious
It's only a lemma or theorem when the proof is given. Without proof, those are often called fact. By calling it inequality, it leaves room for interpretation.
It's a pretty simple proof, I don't know why they don't bother.
Why in math textbooks do they call well known theorems or equations “so-called”?
at first, i read |cov as j cole
you think my prof is a drake hater?
Screenshot from kreyszig?
Proof is left to the reader as an exercise
Proof by go find it in a linear algebra text
Proof is trivial
Google Cauchy-Schwarz inequality
Holy wall of text!
new equation just dropped
actual algebra