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Unformatted text preview: Let W be the subspace spanned by the following u ’s and write y as the sum of a vector in W and a vector orthogonal to W . y = 4 3 3-1 , u 1 = 1 1 1 , u 2 = -1 3 1-2 , u 3 = -1 1 1 BEST APPROXIMATION FACT. The vector ˆ y is the closest vector or point in W to y , that is, || y-ˆ y || < || y-v || for all v ’s in W distinct from ˆ y . THE ORTHONORMAL CASE. If the columns of the matrix U are an orthonormal basis for the subspace W of R n , then proj W y = UU T y . HOMEWORK: SECTION 6.3...
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- Spring '08
- Linear Algebra, orthogonal basis