Unformatted text preview: k R~x k = k ~x k for every ~x ∈ R n . 4. Let { ~v 1 , . . . ,~v n } be an orthonormal basis for an inner product space V with inner product h , i and let ~x = c 1 ~v 1 + · · · + c n ~v n and ~ y = d 1 ~v 1 + · · · + d n ~v n . Show that < ~x,~ y > = c 1 d 1 + · · · + c n d n , and k ~x k 2 = c 2 1 + · · · + c 2 n ....
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 Spring '10
 WILKIE
 Linear Algebra, Matrices, Dot Product, Orthogonal matrix, Inner product space, orthogonal matrices

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