Category:Orthogonal Projections

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This category contains results about Orthogonal Projections.

Let $H$ be a Hilbert space.

Let $K$ be a closed linear subspace of $H$.

Then the orthogonal projection on $K$ is the mapping $P_K: H \to H$ defined by

$k = \map {P_K} h \iff k \in K$ and $\map d {h, k} = \map d {h, K}$

where the latter $d$ signifies distance to a set.