[理工] [工數] [矩陣] 證明特徵值

看板Grad-ProbAsk作者 (阿Ken)時間14年前 (2010/03/22 20:51), 編輯推噓1(1推 0噓 5→)
留言6則, 2人參與, 最新討論串1/1
Show that the eigenvalues of [αβ] are real. [βγ] ------------------------------------------------------ 這題的λ是α和γ沒錯吧?(目測) 請問該怎麼證明它們是實數呢?? 帶數字進去嗎??還是? 題目短短一行卻不知怎麼下筆 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 220.139.149.158
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03/22 20:53, , 1F
A^T X = AX , AX=λX下去證
03/22 20:53, 1F
[αβ]^T [X1] [αX1 βX2] [αβ][X1] [βγ] [X2] = [βX1 γX2] = [βγ][X2] [αβ][X1] [λ1 0][X1] [βγ][X2] = [0 λ2][X2] 故λ1=α λ2=γ β=0 特徵值為實數 (寫對了?) ※ 編輯: iamwwj 來自: 220.139.149.158 (03/22 21:13)
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03/22 21:13, , 2F
謝謝kagato大指點^^
03/22 21:13, 2F
推
03/22 21:18, , 3F
(AX)^T=(λX)^T,X^T*A^T=λ*X^T,X^T(A^T*X)=λ(X^T*X)
03/22 21:18, 3F
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03/22 21:20, , 4F
X^T(AX)=λ'(X^T*X),X^T(λX)=λ'(X^T*X)
03/22 21:20, 4F
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03/22 21:21, , 5F
(λ-λ')X^T*X=0 , λ=λ' , '表示共厄
03/22 21:21, 5F
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03/22 21:43, , 6F
我懂了,寫的很清楚,謝謝kagato大^^
03/22 21:43, 6F
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