Re: [理工] [線代] skew-symmetric matrix

[pikachu123 (pika)]

※ 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



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◆ From: 114.44.172.165
※ 編輯: pikachu123      來自: 114.44.172.165       (02/05 23:25)
→ gskman:呵呵 我是(I-K)(I+K)=I-K^2=(I+K)(I-K) 應該差不多
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→ Jerrynet:黑啊，就是一樓寫的
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