Wedge product/Natural duality/Finite-dimensional/Fact

isomorphism

${\displaystyle \psi \colon \bigwedge ^{k}V^{*}\longrightarrow {\left(\bigwedge ^{k}V\right)}^{*},}$

given by

${\displaystyle {}(\psi (f_{1}\wedge \ldots \wedge f_{k}))(v_{1}\wedge \ldots \wedge v_{k})=\det(f_{i}(v_{j}))_{ij}\,}$

(with ${\displaystyle {}f_{i}\in V^{*}}$ and

${\displaystyle {}v_{j}\in V}$