Hilbert projection theorem
In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector in a Hilbert space and every nonempty closed convex there exists a unique vector for which is minimized over the vectors ; that is, such that for every
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Existence of orthogonal projections onto closed subspaces
The projection theorem states that any vector in a Hilbert space can be uniquely decomposed into a component in a closed subspace and a component orthogonal to it.