Proof of Minkowski Inequality using Cauchy Shwarz

1. Sep 24, 2006

barksdalemc

I tried to expand the [SUM{[X sub k + Y sub k]^2}]^1/2 term but I am stuck there.

2. Sep 24, 2006

river_rat

Okay, first hint

$$|| \vec{x} + \vec{y}||^2 = ( \vec{x}+ \vec{y}, \vec{x}+ \vec{y} )$$

Where $$(\cdot, \cdot)$$ 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
3. Sep 24, 2006

barksdalemc

Got it thanks. Worked out.