# eigenspace question

• Apr 3rd 2008, 12:20 AM
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 $E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V)$ ?
• Apr 3rd 2008, 12:43 AM
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 $E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V)$ ?