Eigenvalues and Eigenvectors

• \(\lambda\in \lambda(A) \Leftrightarrow A-\lambda I \text{ is singular} \Leftrightarrow \text{det}(A-\lambda I)=0\)
• \(\{x\neq0|x\in \mathcal{N}(A-\lambda I)\}\) is the set of all eigenvectors associated with \(\lambda\).  
• \(\mathcal{N}(A-\lambda I)\) is the eigenspace for A.