The best approximation to by elements of a subspace W is given by the vector −projW(). 2. If an ×p matrix has orthonormal columns, then T= for all in ℝ. 3. If W is a subspace of ℝ and if is in both W and W⊥, then must be the zero vector. 4. If =1+2, where 1 is in a subspace W and 2 is in W⊥, then 1 must be the orthogonal projection of onto W. 5. Let 1,2,…, be an orthonormal basis of a vector space . In the Orthogonal Decomposition Theorem, each term =⟨,1⟩1+…+⟨,⟩ is itself an orthogonal projection of onto a subspace of .