問題詳情

3.(19%)下面的問題共有三個子题,(a)子题要清楚地寫出證明,(b)子题只要簡短扼要地回答提问即可,(c)子題除提出答案外、還需寫出答案背後的推導。Let A be any matrix in

. Then, since rank
(A) = dim(R
(A)), the dimension of range of A, andR
(A) = R(AAT), we have the result rank
(A) = rank(AAT). Therefore, when replacing A by its QR factorization, we get rank
(A) = rank(QRRTTQTT).


【題組】(a) (6%) Please continue the argument to derive the result rank
(A) = rank(R). .

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