Re: [理工] [線代] skew-symmetric matrix

看板Grad-ProbAsk作者mp8113f (丹楓)時間14年前 (2012/02/05 22:26)推噓1(1推 0噓 1→)

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※ 引述《vendor47 (屁)》之銘言： : T : Suppose that K is a square matrix with K = -K and that (I-K) is nonsingular; : define : -1 : A = (I+K)(I-K) : Show that A is an orthogonal matrix. : T : 我的想法是讓 AA 是一個 digonal matrix : T : 但我找出 A 後就卡住了... : 請問有高手會這題嗎? : 謝謝 T -1 -1 T AA = [(I+K)(I-K) ][(I+K)(I-K) ] -1 -1 T T = (I+K)(I-K) [(I-K) ] (I+K) -1 T -1 T T = (I+K)(I-K) [(I-K) ] (I + K ) -1 T T -1 = (I+K)(I-K) [I -K ] (I-K) -1 -1 = (I+K)(I-K) [I+K] (I-K) T -1 　 -1 -1 若 A為 orthogonal matrix 則 A = A → [I+K] (I-K) = [I-K] [I+K] 以上不能倒果為因證明XD ... -1 -1 -1 -1 -1 利用另外一個[(I-K)(I+K)] = [I-K] [I+K] = [I+K] [I-K] = I 感謝推文指證 !^^ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 125.224.76.42

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mp8113f

02/05 22:29, , 1^F

02/05 22:29, 1^F

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pikachu123

02/05 23:15, , 2^F

02/05 23:15, 2^F

※ 編輯: mp8113f 來自: 125.224.71.18 (02/06 00:01)

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