Re: [理工] [線代]-正負定
※ 引述《zx33571163 (mm)》之銘言：
: Q on the subspace M={x: x1 + x2+ x3 =0}
: is 正定 負定 不定?
: (2)
: P:M->M
: M在P上代表矩陣A
: 如果A負定 則P在M上負定 如何證明?
1.
M=Span({[1 -1 0]^T , [1 0 -1]^T}) , ^T為轉置
LET V1=[1 -1 0]^T , V2=[1 0 -1]^T
<1> V1^T Q V1 =-2
<2> V2^T Q V2 =-2
<3> LET X=c1V1+c2V2
X^T Q X =c1(-2)+c2(-2) => 正負不定
應該是這樣
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