Vector space/Flag/Definition

Flag

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

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

is called a flag in ${}V$.