[理工] 線代
1. Suppose q1,q2,q3,q4 are orthonormal vectors in R^4.
Let A=[q1 q2 q3 q4], B=[q1+q2 q2+q3 q3+q4 q4+q1]
and C=[q2 q3 q4 q1]. Find all possible values for the 4 by 4 determinats
detA, detB, detA*detC.
我的算法是利用q1 q2 q3 q4彼此獨立所以經由列運算可以轉成單位矩陣
故detA=1,不曉得這樣子想對不對?
2. If A is 3 by 3 symmetric positive definite, then Aqi=λiqi
with eigenvalues λi and orthonormal eigenvectors qi. Suppose
x=c1*q1+c2*q2+c3*q3. Assume λ1<=λ2<=λ3. What c's will make the ratio
x^TAx/(x^Tx) as large as possible? What is the maximum of the ratio
x^TAx/(x^Tx)?
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◆ From: 36.239.247.179
推
02/17 23:36, , 1F
02/17 23:36, 1F
→
02/17 23:52, , 2F
02/17 23:52, 2F
※ 編輯: tokyo291 來自: 36.239.247.179 (02/17 23:54)
推
02/18 00:20, , 3F
02/18 00:20, 3F
→
02/18 00:20, , 4F
02/18 00:20, 4F
→
02/18 00:21, , 5F
02/18 00:21, 5F
※ 編輯: tokyo291 來自: 36.239.247.179 (02/18 00:22)
推
02/18 00:31, , 6F
02/18 00:31, 6F
→
02/18 00:48, , 7F
02/18 00:48, 7F
※ 編輯: tokyo291 來自: 36.239.247.179 (02/18 00:48)
推
02/18 17:44, , 8F
02/18 17:44, 8F
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