QR factorization and the hat matrix Using the QR factorization defined in Appendix A.13, show that H = QQ′. Hence, if qi is the ith row of Q,  This means that if the QR factorization of X has been...

QR factorization and the hat matrix Using the QR factorization defined in Appendix A.13, show that

H = QQ′. Hence, if qi is the ith row of Q,
 This means that if the QR factorization of X has been computed, hii is the sum of squares of the elements of qi, and the less-frequently used off-diagonal elements hij are the sums of products of the elements of qi and qj.