Vector space/Flag/Dual space/Exercise

Let ${}V$ be an ${}n$-dimensional ${}K$-vector space over a field ${}K$, and let

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

denote a flag in ${}V$. Show that the linear subspaces

${}W_{i}:=V_{n-i}^{\perp }\,$

define a flag in the dual space ${}{V}^{*}$.

Create a solution