Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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