Vector space/Flag/Definition

Let ${\displaystyle {}K}$ denote a field, and let ${\displaystyle {}V}$ denote a finite-dimensional vector space of dimension ${\displaystyle {}n=\dim _{K}{\left(V\right)}}$. Then a chain of linear subspaces

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

is called a flag in ${\displaystyle {}V}$.