紫郁风情
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共回答了13个问题采纳率:92.3% 举报
A=
1,0,-1
0,1,0
-1,0.1
|λE-A|=λ³-3λ²+2λ=λ(λ-1)(λ-2)
λ1=0.-x1+x3=0,-x2=0.可取α1=(1/√2,0,1/√2)′
λ2=1,x3=0,x1=0.取α2=(0,1,0)′
λ3=2,x1+x3=0,x2=0.取α3==(1/√2,0,-1/√2)′
取正交变换:(x1,x2,x3,)′=P(y1,y2,y3).其中P=(α1,α2,α3)
即x1=y1/√2+y3/√2.
x2=y2.
x3=y1/√2-y3/√2.
x1²+x2²+x3²-2x1x3
=y1²/2+y1y2+y3²/2+y2²+y1²/2-y1y2+y3²/2-2(y1²/2-y3/2)
=y2²+2y3².
1年前
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