Re: [理工] 線代
: 對所有x,y屬於R^n*1
: T T T
: y A Ax=(Ay)Ax=<Ax,Ay>=1/4||Ax+Ay||-1/4||Ax-Ay||
: T T
: =<x,y>=y x=y Ix
: T
: 得A A=I,所以A is an orthogonal matrix
少幾步...
T T T T T T
<Ay, Ax> = y A Ax = y (A Ax) = <y, A Ax> = y x = < y, x>
T T
y‧A Ax - y‧x = y‧(A Ax - Ix) = 0
因為是對所有x,y都滿足,所以=>
T
A Ax - Ix = 0
T
(A A - I)x = 0
因為是對所有x,y都滿足,所以=>
T
A A - I = 0
T T T
=> A A = I => 若A為方陣 => A A = A A = I => A為orthogonal matrix
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※ 編輯: cha122977 來自: 123.193.250.155 (10/13 23:02)
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