Proof of Minkowski Inequality using Cauchy Shwarz

[barksdalemc]

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

 

[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.

 

[barksdalemc]

Got it thanks. Worked out.