Unformatted text preview: = ± x 1 x 2 x 3 ² G y 1 y 2 y 3 c) Consider the inner product h , i for P 2 deﬁned by h p,q i = p (0) q (0) + p (1) q (1) + p (2) q (2). Determine the matrix G of this inner product with respect to the basis { 1 ,x,x 2 } . 4. Let V be a real inner product space with inner product h , i and let ~u,~v ∈ V . Prove that k ~u + ~v k 2 = k ~u k 2 + k ~v k 2 if and only if h ~u,~v i = 0....
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 Spring '10
 WILKIE
 Vectors, Matrices, Dot Product, Orthogonal matrix, inner product, Inner product space

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