Eigenspace

Let $\lambda$ be an eigenvalue of $A\in M_{n\times n}(\mathbb{R})$. The set containing all of the eigenvectors of $A$ corresponding to $\lambda$ together with the zero vector of ${\mathbb{R}}^n$ is called the eigenspace of $A$ corresponding to $\lambda$, and is denoted by $E_{\lambda }(A)$. It follows that $E_{\lambda }(A)=Null(A-\lambda I)$

The algebraic multiplicity $a_{\lambda }$ of $\lambda$ is the number of times $\lambda$ appears as a root of $C_A(\lambda )$. The geometric multiplicity $g_{\lambda }$ of $\lambda$ is the dimension of the eigenspace $E_{\lambda }(A)$.

Related

• Eigenvalues and Eigenvectors