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Best Approximation: The Perpendicular Wins

0:35Fortellerstemme
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Best approximation theorem — the closest point in a subspace to a given vector is its orthogonal projection. A point u above a line L: dropping a perpendicular hits the foot uniquely, and any other candidate on the line is strictly farther by Pythagoras.

best approximationorthogonal projectionsubspacePythagorasminimum distance
ForutsetterProjection onto a LineGram-Schmidt: Subtract the Projection
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