[微方] 證明題

看板Math作者 (坦帕灣光芒)時間13年前 (2012/03/19 18:01), 編輯推噓3(304)
留言7則, 2人參與, 最新討論串1/1
Ax=b when det A=0 (a)Suppose that A is a real-valued n*n matrix.Show that (Ax,y)=(x,A的轉置y)for any vectors x and y. (b)If A is not necessary real, show that (Ax,y)=(x,A*y)for any vectors x and y. (*不是乘,是A*乘y) (c)If A is Hermitian, show that (Ax,y)=(x,Ay)for any vectors x and y. 順便借問一題線代 ┌-1 4 2 ┐ ┌ 1-2-1 ┐ A=│-1 3 1 │ eigenvalue=1→ A-I=│ 0 0 0 │ └-1 2 2 ┘ └ 0 0 0 ┘ ┌ 0 3 1 ┐ ┌ 1 0 0 ┐ B=│-1 3 1 │ eigenvalue=1→ B-I=│ 0 1 0 │ └ 0 1 1 ┘ └ 0 0 0 ┘ A的rank=1 dim EA(1)=2 B的rank=2 dim EB(1)=1 請問dim要怎麼看?? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.43.154.238

03/19 20:01, , 1F
dim就算不知道..看你寫的也猜的出來吧..dim=n-rank
03/19 20:01, 1F

03/19 20:05, , 2F
嗯 謝謝 我也是這樣猜的 想確定一下
03/19 20:05, 2F

03/19 21:02, , 3F
但我查資料(太久沒碰了)rank(A)=2=dim(A)=2...
03/19 21:02, 3F

03/19 21:03, , 4F
rank叫秩,dim叫維度...那EA(1)是指A-I嗎..如果是那
03/19 21:03, 4F

03/19 21:03, , 5F
dim應該只剩1.....
03/19 21:03, 5F

03/19 21:08, , 6F
抱歉...算錯...rank(A)=3=dim(A)....
03/19 21:08, 6F

03/19 23:46, , 7F
對 EA(1)是指A-I
03/19 23:46, 7F
文章代碼(AID): #1FPmFpdU (Math)