1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Cauchy Schwarz Proof Question

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that |x'y| <= ||x|| ||y|| for vectors x, y

    2. Relevant equations
    ||x|| is the norm of x
    x' is the transpose of x

    3. The attempt at a solution
    ||(x/||x||)-(y/||y||)|| = [ (x'/||x|| - y'/||y||)(x/||x|| - y/||y||) ]^1/2 = [-1/(||x||*||y||) (x'y + y'x) +2]^1/2
    we know that this norm is positive or zero, so:
    [-1/(||x||*||y||) (x'y + y'x) +2]^1/2 > 0
    -> x'y + y'x < 2||x||||y||
    x'y = y'x because they are scalars and the transpose of a scalar doesn't change its value
    -> 2x'y < 2||x||||y||
    -> x'y < ||x||||y||

    My result doesn't have absolute values around x'y; what am I doing wrong?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted