Linear Algebra Done Right
《Linear Algebra Done Right》 · 第 300 页 · Section 8A「Generalized Eigenvectors and Nilpotent Operators」，Definition 8.8
Suppose $T\in\mathcal L(V)$ and $\lambda$ is an eigenvalue of $T$. A vector $v\in V$ is called a generalized eigenvector of $T$ corresponding to $\lambda$ if $v\ne0$ and $(T-\lambda I)^kv=0$ for some positive integer $k$.