Use the inner product
⟨f,g⟩=∫10f(x)g(x)dx
in the vector space C0[0,1] of continuous functions on the domain [0,1] to find the orthogonal projection of f(x)=3x2−2 onto the subspace V spanned by g(x)=x and h(x)=1. (Caution: x and 1 do not form an orthogonal basis of V.)
projV(f)= .\n | |