Unformatted text preview: 5. Show that if f : R n → R is a function that satisﬁes the following conditions − f ( v ) ≥ 0 for all v ∈ R n − f ( v ) = 0 iﬀ v = 0 − f ( αv ) =  α  f ( v ) for all α ∈ R and all v ∈ R n − The set { v : f ( v ) ≤ 1 } is convex then f deﬁnes 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 Hölder’s inequality for part of the proof....
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 Fall '10
 Chandrashekharan
 Linear Algebra, Invertible matrix, rank matrix, column rank matrix

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