Re: [理工] [線代] eigenvalue是非兩題
※ 引述《juan19283746 (小阮)》之銘言：
: 標題: [理工] [線代] eigenvalue是非兩題
: 時間: Thu Dec 9 16:55:39 2010
:
:
: 1. If A is the zero matrix , then the only eigenvalue of A is 0.
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: → juan19283746:那請問一下 如果第一題條件改成A^2是零矩陣 12/09 19:22
: → juan19283746:特徵值還會都是0嗎 謝謝 12/09 19:23
: → BenLinus:我覺得會 @@ 12/09 20:05
2 2
A = 0 => det(A) = 0 = det(A)det(A)
2
[det(A)] = 0, det(A) = 0 = det(A - λI) => λ 可以為 0
不過再考慮 det(A) = det(A - λI), 拿個 2x2 的矩陣來說好了,
假設 A = [ a b ] det(A) = ad -bc 2
[ c d ] det(A - λI) = (a-λ)(d-λ) - bc = ad - (a+d)λ +λ -bc
若 det(A) = det(A - λI),
2
-(a+d)λ +λ = 0 => 用公式解求得 λ = (a+d) or 0
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◆ From: 1.160.138.81
※ 編輯: BenLinus 來自: 1.160.138.81 (12/09 20:32)
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