# eigenspace question

• April 2nd 2008, 11:20 PM
lllll
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 $E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V)$ ?
• April 2nd 2008, 11:43 PM
mr fantastic
Quote:

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