→ mp8113f:最後一步我把題目要證的拿來輔助 不知是否可行QQ" 02/05 22:29
推 pikachu123:當然不行倒果為因了 02/05 23:15
※ 編輯: mp8113f 來自: 125.224.71.18 (02/06 00:01)
※ 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 !^^
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