Generalized Eigenvector

An eigenvector used when the Geometric Multiplicity is less than the Algebraic Multiplicity, and we need more vectors to form a Basis. Often used to create Jordan Basis.

Definition

• With eigenvector $v$ and eigenvalue $\lambda$
• The generalized eigenvector $v^{\prime }$ is a solution for $(A-\lambda I)v^{\prime }=v$