Algebraic and Analytic Geometry
《Algebraic and Analytic Geometry》 · 第 484-485 页 · Section 7.1「The Jordan Canonical Form I」，Definition
Definition. Let $T$ be a linear operator on a vector space $V$, and let $\lambda$ be an eigenvalue of $T$. The generalized eigenspace of $T$ corresponding to $\lambda$, denoted $K_\lambda$, is the subset of $V$ defined by $K_\lambda=\{x\in V:(T-\lambda I)^p(x)=0\text{ for some positive integer }p\}$.