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看板Grad-ProbAsk作者 (麵包)時間16年前 (2010/02/25 00:12), 編輯推噓4(401)
留言5則, 5人參與, 最新討論串1/1
1. suppose A is an n*n matrix with the property that A^2=A. Let a1,a2,...,an 屬於 R^n be the column vectors of A and A1,...,An 屬於 R^n be the row vectors of A. Let C(A) = span(a1,...,an) and R(A) = span(A1,...,An) be the column space and the row space of A, respectively. Define E(A) = {x 屬於 R^n|x=Ax} F(A) = {x 屬於 R^n|x=u-Au for some u 屬於 R^n} Find the following four sets: C(A) 交集 E(A),N(A) 交集 F(A),C(A) 交集 N(A), C(A)+N(A). 2. 假設A,B 屬於 R^(n*n),若A,B正交相似 則 A為正定矩陣 <=> B為正定矩陣 成立嗎 請各位幫忙 感謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 220.131.66.196

02/25 00:27, , 1F
!_!
02/25 00:27, 1F

02/25 08:16, , 2F
2.相似eigenvalue就會一樣,都會大於0
02/25 08:16, 2F

02/25 09:06, , 3F
1. C(A)=E(A),N(A)=F(A) 所以答案依序 C(A),N(A),{0},R
02/25 09:06, 3F

02/25 12:00, , 4F
請問為什麼N(A)=F(A)@@
02/25 12:00, 4F

02/25 13:28, , 5F
x=u-Au , Ax=A(u-Au)=Au-A^2u=Au-Au=0
02/25 13:28, 5F
文章代碼(AID): #1BXL0521 (Grad-ProbAsk)