Re: [理工] [線代] 內積空間

看板Grad-ProbAsk作者Byzantin (拜占庭)時間14年前 (2011/11/24 21:29)推噓4(4推 0噓 1→)

留言5則, 3人參與討論串4/4 (看更多)

(a) x =/= 0 , <x,x> = (Ax)^T(Ax) > 0 , 令 Ax = [ x1,x2,x3 ... xn]^T <x,x> = x1^2 + x2^2 + ... + xn^2 > 0 => x1,x2...xn 不全為0 也就是Ax =/= 0 A若可逆則Ax = 0 只有當x = 0才成立因此A要可逆 (b) A : n*n x : n*1 Ax : n*1 (Ax)^T : 1*n (Ax)^T(Ay) : 1*1 ，所以(Ax)^T(Ay) = ((Ax)^T(Ay))^T 希望沒錯QQ ※ 引述《askaleroux (aska)》之銘言： : Let the elements of an inner product space V be all vectors in R^n : Define as : <x,y> = (Ax)^T(Ay) where A is an n*n matrix : (a) What is the most genera; matrix A such that above is an inner product : => A必須可逆(Why????) : (b) What are the properties stated in (a) ? : 其中 : <x,y> = (Ax)^T(Ay) = ((Ax)^T(Ay))^T = (Ay)^T(Ax) : 為什麼忽然加了一個轉置還會相等？ : ============================================================= : 有請大大姐答 : 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.195.193.134

推

wheels

11/24 21:34, , 1^F

11/24 21:34, 1^F

推

ntust661

11/24 21:40, , 2^F

11/24 21:40, 2^F

推

wheels

11/24 21:40, , 3^F

11/24 21:40, 3^F