Re: [理工] [線代] skew-symmetric matrix

看板Grad-ProbAsk作者pikachu123 (pika)時間14年前 (2012/02/05 23:22)推噓1(1推 0噓 4→)

留言5則, 3人參與討論串3/3 (看更多)

※ 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 t -1 A A= [(I+K)(I-K) ] [(I+K)(I-K) ] t [ -1] t = [ (I-K) ](I+K) (I+K)(I-K) t [ -1] -1 = [ (I-K) ](I-K)(I+K)(I-K) (note:I+K I-K可交換) t [ -1] -1 = [ (I-K) ](I+K)(I-K)(I-K) t [ -1] = [ (I-K) ](I+K) -1 [ t] -1 = [ (I-K) ](I+K)=(I+K) (I+K)=I -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.44.172.165 ※ 編輯: pikachu123 來自: 114.44.172.165 (02/05 23:25)

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gskman

02/05 23:26, , 1^F

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mp8113f

02/05 23:54, , 2^F

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mp8113f

02/05 23:57, , 3^F

02/05 23:57, 3^F