Linear mapping/Invariant flag/Definition

Invariant flag

Let ${}V$ be a vector space of dimension ${}n$, and let

$f\colon V\longrightarrow V$

be a linear mapping. A flag

${}0=V_{0}\subset V_{1}\subset \ldots \subset V_{n-1}\subset V_{n}\,$

is called ${}f$-invariant, if ${}f(V_{i})\subseteq V_{i}$ holds for all ${}i=0,1,\ldots ,n-1,n$.