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According to the Projection Theorem, if W is a finite dimensional subspace of an inner
product space V , then every vector u ∈ V can be expressed uniquely as
u = w1 + w2 ,
where w1 ∈ W and w2 is orthogonal to W . The vector w1 is called the orthogonal projection of u on W and is denoted by w1 = projW u.