Re: [線代] 請問這個證明的直證法
※ 引述《znmkhxrw (QQ)》之銘言：
: 想請問這個性質有沒有直接的證法, 我證的有點迂迴...
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: 令A€M_mxn(F), F = R or C, b€range of A
: 則 Ax = b <=> A^*A x = A^*b, 其中A^*是A的transpose conjugate
Let Ay=b. Apply inner product with z on both sides of the equation
A^*Ax = A^*b and use the adjoint property, we get
<Ax,Az> = <b,Az>, or <Ax-b,Az> = 0 for all possible z.
As Ax-b = Ax - Ay = A(x-y), taking z = x-y yields A(x-y) = 0.
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有時數學真的很難。拿來跟人聊天，你講maximum principle只會被別人覺得噁心。
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06/16 04:39,
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06/16 09:48,
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