Linear mapping/Invariant flag/Definition

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

${\displaystyle f\colon V\longrightarrow V}$

be a linear mapping. A flag

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

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