Generalized Eigenvector

An eigenvector used when the Geometric Multiplicity is smaller than the Algebraic Multiplicity of a Eigenspace. This vector will allow for construction of Basis to create a Jordan Basis.

Definition

• With a Eigenvector $v$ and associated Eigenvalue $\lambda$
• A generalized eigenvector $v^{\prime }$ is the solution to $(A-\lambda I)v^{\prime }=v$