Let W is a finite dimensional subspace of an inner product space V and y is any vector in V. The best approximation to y from W is then Proj, , i.e for every w (that is not Proj, ) in W, we have y-Proj:|<[y-w.

Let W is a finite dimensional subspace of an inner product space V and y is any vector in V. The best approximation to y from W is then Proj, , i.e for every w (that is not Proj, ) in W, we have y-Proj:|<[y-w.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Question

Best Approximation Theorem
Let W is a finite dimensional subspace of an inner product space V and y is
any vector in V. The best approximation to y from W is then Pr oj", , i.e for every w (that
is not Proj, ) in W, we have
y- Proj:|| < |y- w||.

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