Unformatted text preview: distances. Once we know what an inner product should be, there are multiple examples of such inner products, including new ones on R n and P 7 . We discuss just one, but it’s probably the most useful and pervasive. The vector space C [0 , 1] consists of all continuous functions deﬁned on the interval [0 , 1]. For two such functions f and g , deﬁne the inner product of f and g to be h f, g i = Z 1 f ( t ) g ( t ) dt. EXAMPLES. (1) Compute h f, g i , where f ( t ) = 2 + 3 t and g ( t ) = t + 1. Then compute  f  , the projection of g onto f , and a vector/function h so that h is orthogonal to f . HOMEWORK: SECTION 6.7, #21, 22, 23, 24, 25...
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 Spring '08
 PAVLOVIC
 Approximation, Matrices, Vector Space, Dot Product, inner product, Inner product space

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