5.16 For any matrix X of full rank, the projectionmatrix onto L(X), the linear space spanned by the columns of X, is defined as PX = X(X



X)

−1X

 (the definition can be generalized even if X is not of full rank). The orthogonal projection to L(X) is defined as PX

⊥ = I − PX, where I is the identity matrix. Show that PX ≥ 0 and PX

⊥ ≥ 0.