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: Proof of Minkowski Inequality using Cauchy Shwarz

  1. Sep 24, 2006 #1
    I tried to expand the [SUM{[X sub k + Y sub k]^2}]^1/2 term but I am stuck there.
  2. jcsd
  3. Sep 24, 2006 #2
    Okay, first hint

    [tex] || \vec{x} + \vec{y}||^2 = ( \vec{x}+ \vec{y}, \vec{x}+ \vec{y} ) [/tex]

    Where [tex] (\cdot, \cdot) [/tex] is the inner product on your inner product space. So you should not have any square roots to worry about. Expand the inner product, then use the Cauchy-Swartz inequality.
    Last edited: Sep 24, 2006
  4. Sep 24, 2006 #3
    Got it thanks. Worked out.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook