Eigenspace

linear-algebra

Definition

Eigenspace

Let $T:V\to V$ be a linear operator and let $\lambda$ be an eigenvalue of $T$. The eigenspace of $T$ for $\lambda$ is the set

$$E_{\lambda }=\{x\in V:Tx=\lambda x\}$$

Equivalently, $E_{\lambda }$ is the kernel of $T-\lambda I$:

$$E_{\lambda }=\ker (T-\lambda I)$$