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-   -   Cauchy/ Triangle Inequality (http://www.physicsforums.com/showthread.php?t=439915)

 Design Oct20-10 09:53 AM

Cauchy/ Triangle Inequality

I was wonder what conditions a and b have to be for each inequality in order to satifsy the equality?

 mathman Oct20-10 03:54 PM

Re: Cauchy/ Triangle Inequality

Quote:
 Quote by Design (Post 2942884) I was wonder what conditions a and b have to be for each inequality in order to satifsy the equality?
It would help if you wrote out the inequality as a function of a and b. I'm not a mind reader.

 Design Oct21-10 09:23 AM

Re: Cauchy/ Triangle Inequality

Cauchy's inequality is just the trivial |a . b| <= |a||b| Oo

Triangle inequality

|a+b| = |a| +|b|

 ╔(σ_σ)╝ Oct21-10 09:32 AM

Re: Cauchy/ Triangle Inequality

What do you think happens when a,b are both postive or both negative ?

 Landau Oct21-10 02:05 PM

Re: Cauchy/ Triangle Inequality

Just go over the proof, and you'll probably see it.

 mathman Oct21-10 03:56 PM

Re: Cauchy/ Triangle Inequality

Quote:
 Quote by Design (Post 2944642) Cauchy's inequality is just the trivial |a . b| <= |a||b| Oo Triangle inequality |a+b| = |a| +|b|
To answer your question, you need to specify what a and b are. Possibilities: real numbers, complex numbers, vectors (either real or complex).

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