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Math Help - eigenspace question

  1. #1
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    eigenspace question

    Prove that the eigenspace of T corresponding to \lambda is the same eigenspace of T^{-1} corresponding to \lambda^{-1}.

    I just want to know how do you show an eigenspace of T corresponding to \lambda ?

    would it just be E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V) ?
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  2. #2
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    Quote Originally Posted by lllll View Post
    Prove that the eigenspace of T corresponding to \lambda is the same eigenspace of T^{-1} corresponding to \lambda^{-1}.

    I just want to know how do you show an eigenspace of T corresponding to \lambda ?

    would it just be E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V) ?
    I think this link will answer your question.
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