Consider eq 518b where g and btnbspare orthogonally rotated

Question

Consider Eq. (5.18b) where G and B^T are orthogonally rotated components and loadings respectively (Theorem 5.2a). Show that the new scores G are orthogonal to the residuals δ.

THEOREM 5.2

Let X = Z_(r) P^T_(r) +δ be a PC model and let X =V_(T) Q^T_(r) + δ as in Eq. (5.17). Then

(i) Predicted values  and their sum of squares remain unchanged by T.