3.2 ( ) Show that the matrix (T)1T (3.103) takes any vector v and projects it onto the space spanned by the columns of .

3.2 ( ) Show that the matrix

Φ(ΦTΦ)−1ΦT (3.103)

takes any vector v and projects it onto the space spanned by the columns of Φ. Use this result to show that the least-squares solution (3.15) corresponds to an orthogonal projection of the vector t onto the manifold S as shown in Figure 3.2.