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Definition: Suppose that our given form is nondegenerate on a subspace W and that V is a direct sum of W and its orthogonal complement, W perp. Then every vector in V can be written uniquely in the form v=w+u, with w in W and u in W perp. The orthogonal projection from V to W is the map f: V -> W defined by f(v)=w.
Source: Algebra, second edition by Michael Artin