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Math Help - matrix prove

  1. #1
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    matrix prove

    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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  2. #2
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    Re: matrix prove

    Quote Originally Posted by yanirose View Post
    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.
    Thanks from yanirose
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  3. #3
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    Re: matrix prove

    Quote Originally Posted by yanirose View Post
    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.
    Thanks from yanirose
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