Hi, all Can I ask a question? If B = P^-1AP and Pv is an eigenvector of A then v is an eigenvector of B I changed it to PB = AP and PBv = APv. After that, what can I do? I am sorry to bother you!
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Originally Posted by yanirose After that, what can I do? Use the fact that Pv is an eigenvector of A. I wouldn't multiply B = P^(-1)AP by P.
Originally Posted by yanirose Hi, all Can I ask a question? If B = P^-1AP and Pv is an eigenvector of A then v is an eigenvector of B I changed it to PB = AP and PBv = APv. After that, what can I do? I am sorry to bother you! $Pv$ is an eigenvector of $A$ so $A(Pv) = \lambda(Pv)$ $Bv = P^{-1} A Pv = P^{-1}\lambda (Pv) = \lambda P^{-1}Pv = \lambda v$ $Bv = \lambda v \Rightarrow v$ is an eigenvector of B.
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