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July 8th, 2017, 05:12 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,641 Thanks: 119  Cauchy Schwarz Inequality
Cauchy Schwarz Inequality in Rn: $\displaystyle x\cdot y\leq xy$ Proof: $\displaystyle \left  x\cdot \frac{y}{y}\right \leq x$ Explanation: $\displaystyle \frac{y}{y}$ is a unit vector which can be expanded to a basis. Then either x is in the direction of y and equality holds, or it has a component among the rest of the basis in which case it's component along y is less than x. 
July 9th, 2017, 05:18 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
What was your purpose in posting this? Do you have a question about it?

September 26th, 2017, 10:30 PM  #3  
Senior Member Joined: Sep 2016 From: USA Posts: 535 Thanks: 306 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
 

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