Unformatted text preview: v k ∈ U . The aﬃne subspace generated by v 1 , v 2 , . . . , v k is the set of all aﬃne combinations of v 1 , v 2 , . . . , v k . A vector u is an convex combination of vectors v 1 , v 2 , . . . , v k when there are nonnegative scalars c 1 , c 2 , . . . , c k so that c 1 + c 2 + . . . + c k = 1 and u = c 1 v 1 + c 2 v 2 + . . . + c k v k . The convex hull of v 1 , v 2 , . . . , v k is the set of all convex combinations of v 1 , v 2 , . . . , v k . A nonempty set U of vectors is an convex set when U contains all convex combinations of vectrors v 1 , v 2 , . . . , v k ∈ U . The parallelopiped spanned by v 1 , v 2 , . . . , v k is the set of all linear combinations u = c 1 v 1 + c 2 v 2 + . . . + c k v k where 0 ≤ c i ≤ 1 for all i = 1 , 2 , . . . , k ....
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 Winter '09
 Wilson
 Linear Algebra, Algebra, Vectors, Scalar, Vector Space, Linear combination, vk, Convex combination

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