[理工] [線代] 矩陣的秩

看板Grad-ProbAsk作者 (Larry)時間11年前 (2012/10/16 22:20), 編輯推噓1(103)
留言4則, 3人參與, 最新討論串1/2 (看更多)
1.Let A,B be 2x2 matrices over R with AB=0 and BA!=0 . Determine the rank of BA. 2.Let A be m by n matrix,P be an inervertible m by m matrix, and Q be an n by n matrix. Which of the following is true? (1)rank(AQ)=nullity(A) (2)rank(AQ)=rank(A) (3)rank(PA)=rank(P) (4)rank(PA)=rank(A) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 59.127.250.83

10/16 22:21, , 1F
想請問一下第二題的(2)
10/16 22:21, 1F

10/16 22:24, , 2F
1.題目給AB=O? 這樣rank(AB)=0吧?
10/16 22:24, 2F

10/16 22:24, , 3F
2.(4)為True
10/16 22:24, 3F

10/16 23:00, , 4F
rank(AB) <= min(rank(A), rank(B)), 所以(2)不一定true
10/16 23:00, 4F
※ 編輯: movo11 來自: 59.127.250.83 (10/17 16:42)
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