老师我想问一下 设a是n元列向量,a^Ta=k,A=aa^T,证明A^m+1=k^mA

A=aa^T,

A^m+1=aa^T^m+1

=aa^Taa^Taa^Taa^Taa^T.

=a(a^Ta)(a^Ta)(a^Ta)(a^Ta)(a^T...

=akkkkkkkkkk..a^T

=kkkkkkkkk(aa^T)

=kkkkkkkkkkA

=k^mA