Eigenspaces

[!Definition 8.3.1]

Let $\lambda \in \mathbb{R}$ be an eigenvalue of $A\in M_{nxn}(\mathbb{R})$. The eigenspace of A corresponding to $\lambda$ is the set

$E_{\lambda }=Null(A-\lambda I)$

[!Definition 8.3.12]

For any eigenvalue $\lambda$ of A,

$1\le g_{\lambda }\le a_{\lambda }\le n$