Solution
= Solution
Pairing $\alpha_i=\sum_jc_{ij}\omega_j$ with $\alpha_k^\vee$ gives $c_{ik}=A_{ik}$. Hence the relation between the two bases is
$$
\boxed{\alpha_i=\sum_jA_{ij}\omega_j}.
$$
= Solution
Pairing $\alpha_i=\sum_jc_{ij}\omega_j$ with $\alpha_k^\vee$ gives $c_{ik}=A_{ik}$. Hence the relation between the two bases is
$$
\boxed{\alpha_i=\sum_jA_{ij}\omega_j}.
$$