
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 8th, 2017, 04:12 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,364 Thanks: 100  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: 3,165 Thanks: 867 
What was your purpose in posting this? Do you have a question about it?

September 26th, 2017, 09:30 PM  #3  
Senior Member Joined: Sep 2016 From: USA Posts: 379 Thanks: 205 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
 

Tags 
cauchy, inequality, schwarz 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cauchy Schwarz Inequality Equality  zylo  Real Analysis  1  June 30th, 2017 06:26 AM 
CauchyBunyakovskySchwarz inequality for preinner product  mozganutyj  Algebra  0  January 12th, 2014 04:45 AM 
CauchySchwarz inequality  jugger3  Linear Algebra  2  August 21st, 2013 02:00 PM 
Insight to the cauchyschwarz inequality  aaronmath  Calculus  3  February 5th, 2012 08:50 AM 
cauchyschwarz?  ElMarsh  Algebra  8  September 21st, 2009 01:24 PM 