申論題

3.(11%)下面的問题共有二個子題,(1)子題要清楚地寫山證明,(b)子題只要簡短扼要地回答 提問即可。 Let A be any matrix in . Then, since rank(A) = dim(R(A)), the dimension of range of A, and R(A) = R(AA^T), we have the result rank(A) = rank(AA^T). Therefore, when replacing A by its QR factorization, we get rank(A) = rank(QRR^TQ^T).