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Unformatted text preview: , 1]. Dene an inner product on X by ( f,g ) = Z 1 f ( t ) g ( t ) dt. Let Y be the subspace of X spanned by f ,f 1 ,f 2 ,f 3 , where f k ( x ) = x k . Find an orthonormal basis for Y . (6) Let Y be a subspace of a Euclidean space X , and P Y : X X the orthogonal projection onto Y . Prove that P * Y = P Y . (7) Show that a matrix M is orthogonal i its column vectors form an orthonormal set. (8) Let X be an ndimensional real Euclidean space, and A : X X a linear map. Dene the map f : X X by f ( x,y ) = x T Ay . Give (with proof) necessary and sucient conditions on A for f to be an inner product on X ....
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This note was uploaded on 03/11/2012 for the course MTHSC 853 taught by Professor Staff during the Spring '08 term at Clemson.
 Spring '08
 Staff
 Linear Algebra, Algebra

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