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Unformatted text preview: 5. Show that if f : R n R is a function that satises the following conditions f ( v ) 0 for all v R n f ( v ) = 0 i v = 0 f ( v ) =   f ( v ) for all R and all v R n The set { v : f ( v ) 1 } is convex then f denes a norm on R n . 6. Show that for p 1 and p 1 + q 1 = 1, k x k p = max y 6 =0  y T x  k y k q , x R n . Hint : You can use Hlders inequality for part of the proof....
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 Fall '10
 Chandrashekharan

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