推 iyenn:!_! 02/25 00:27
推 luckysky1:2.相似eigenvalue就會一樣，都會大於0 02/25 08:16
推 polomoss: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
推 vivaptt:請問為什麼N(A)=F(A)@@ 02/25 12:00
→ Lukewind:x=u-Au , Ax=A(u-Au)=Au-A^2u=Au-Au=0 02/25 13:28
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
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