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Unformatted text preview: orthogonal projection of y onto W, and write proj w y 1 Ex : Let u 1 = 1 5 2 , u 2 = 1 1 2 , y = 3 2 1 , and W = Span { u 1 , u 2 }. Write y as the sum of a vector in W and a vector orthogonal to W. The Best Approximation Theorem Let W be a subspace of n , y any vector in R n , and y the orthogonal projection of y onto W. Then y is the closest point in W to y , in the sense that y – y < y – v for all v in W distinct from y . y is called the best approximation to y by elements of W 2 Ex : Let u 1 = 1 5 2 , u 2 = 1 1 2 , y = 3 2 1 , and W = Span { u 1 , u 2 }. Find the closest point in W to y and the distance from y to W 3...
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 Spring '08
 Johnson,J
 Linear Algebra, Algebra, orthogonal basis, Orthogonal Decomposition Theorem, Generalized Orthogonal projections

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