作者smartlwj (实变我好爱你)
看板Grad-ProbAsk
标题Re: [理工] 矩阵一问
时间Fri Mar 27 21:57:08 2009
※ 引述《xvxvxvxvxvxv (大东)》之铭言：
: http://www.wretch.cc/album/show.php?i=tvvshow59887&b=1&f=1580206611&p=0
: 有高手能帮我解一下第七题的第二小题吗?
: X分离不出
: 感激不尽
A = [4 3]
[5 6]
det(A-xI) = (x-1)(x-9)
=> eigenvalues of A are 1 and 9
T
V(1) = ker(A-I) = span{[1 -1] }
T
V(9) = ker(A-9I) = span{[3 5] }
-1
Set P = [ 1 3] such that P AP = D = [1 0]
[-1 5] [0 9]
-1 -1 -1 -1
=> A = PDP = P√D√DP =(P√DP )(P√DP )
-1 2
Let X = P√DP , then A = X
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