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July 8th, 2017, 04:12 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,134 Thanks: 88  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, 04:18 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,656 Thanks: 681 
What was your purpose in posting this? Do you have a question about it?


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cauchy, inequality, schwarz 
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