eigenspace question

**lllll** · April 2nd 2008, 11:20 PM

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 $E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V)$ ?

**mr fantastic** · April 2nd 2008, 11:43 PM

Originally Posted by lllll

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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