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.