generalized eigenvector

A vector one differentiation-step removed from an ordinary eigenvector, used when a repeated eigenvalue has too few eigenvectors of its own.

A generalized eigenvector $\mathbf{w}$ for eigenvalue $\lambda$ solves $(A-\lambda I)\mathbf{w}=\mathbf{v}$ for an actual eigenvector $\mathbf{v}$ of $\lambda$ -- supplying the missing independent solution a repeated eigenvalue with only one eigenvector can't produce on its own.