what is cauchy-schwarz? (1 Viewer)

[Logix]

i read in a thread about "cauchy-schwarz", and i have no idea what that is. can some1 pls explain?

 

[turtle_2468]

i read in a thread about "cauchy-schwarz", and i have no idea what that is. can some1 pls explain?

Cauchy-Schwarz is an inequality (C-S) for short. It goes, for positive integer n and positive (can make it non-negative, but positive makes things easy to understand) x_i and y_i...
{(x_1)^2+(x_2)^2+....+(x_n)^2}{(y_1)^2+(y_2)^2+....+(y_n)^2}>={(x_1.y_1)^2+(x_2.y_2)^2+....+(x_n.y_n)^2}
Equality occurs when x_i/y_i=c for some c constant.
It makes life easy for proving many inequalities, but I don't think it's used in 4U at all... ie you can't even assume it... so this is just for interest..

 

[Logix]

ok...................................................
this is way above my head i didnt understand a word u said. luckily its not part of the 4 unit course

 

[turtle_2468]

x_1 is just a number...
so basically you plug numbers into those weird looking symbols
eg if x_1=2, x_2=5, y_1=3, y_2=7
then cauchy-schwarz inequality says that
(2^2+5^2)*(3^2+7^2)>=(2*3+5*7)^2.
Which if you expand out you can see is true.
PS x^2 means x squared...

 

[Logix]

thx for the explanation
wat is x_1? is it x-1? im not used to reading symbols like _, ^, etc

 

[Lazarus]

x_1 is just x₁

and x^2 is just x²

 

[Estel]

Some day you've got to show me how to do that

 

[turtle_2468]

testing $x_1$

 

[turtle_2468]

trying to figure out how to activate it..

 

[CrashOveride]

Interestingly, the last question of the inequalities exercise in my book happens to be:

Prove: (x² + y² + z²)(a² + b² + c²) >= (ax + by + cz)²

 

[Slidey]

Hypertext markup language is enabled in this forum. Use the tags: @sub@ and a subsequent closing tag to make a subscript, and @sup@ with a closing tag to make a superscript, where @ is < or >

example:

x<sub>1</sub>

produces: x₁

 

[turtle_2468]

ahh... many thanks slide.
testing:
x₂
<bold>isn't this cool?</bold>

 

[withoutaface]

There was actually a stickied thread with this stuff in it http://www.boredofstudies.org/community/showthread.php?t=7127

 

[CrashOveride]

http://mcraefamily.com/MathHelp/BasicNumberIneqCauchySchwarz.htm

For anyone interested, straight forward derivation of C-S inequality.

 

[Estel]

x₂
x²

 

[withoutaface]

x^{2^{2^{2^{2^2²22}2}2}2}2_{2_{2_{2_{2_2₂22}2}2}2}

 

[mojako]

Now, can somebody do this?
(don't cheat by looking at my code)
(actually you can't cheat hahaha.. thanks to BoS system)

^hello

 

[Xayma]

<marquee> Why yes sir, I think I can. </marquee>

 

[mojako]

<marquee><b>Why why why...</b></marquee>
<br>
<marquee>Why does HTML code show up in emails??</marquee>

 

[McLake]

Enough with the tags guys