设a=[1,0,1]T,A=ααT,n是正数,则|aE-An|=_________.

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问题 设a=[1,0,1]T,A=ααT,n是正数,则|aE-An|=_________.

选项

答案a2(a-2n)

解析 A=ααT=
αTα=[1,0,1]=2,
An=(ααT)n=ααTααT…ααT=α(αTα)(αTα)…(αTα)αT=2n-1A,

=a[(a-2n-1)2-(-2n-1)2]
=a(a2-a2n)=a2(a-2n).
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