\[ \newcommand{\d}{\mathrm{d}} \newcommand{\e}{\mathrm{e}} \newcommand{\i}{\mathrm{i}} \]

Given a local or global frame \((E_1, \ldots, E_n)\). Then the corresponding local or global coframe is defined by

\begin{equation*} \epsilon^i(E_j)=\delta^i_j. \end{equation*}

If a coframe is given we find a frame with the same procedure.