Let $V$ be a vector space (typically $V=T^*_p M$). Given linearly independent elements $v_1, \ldots, v_p \in V$ and provided that $w_1, \ldots, w_p$ are such that
$$ v_{1} \wedge w_{1}+\cdots+v_{p} \wedge w_{p}=0 $$in $\Lambda V$ then there exist scalars $h_{ij}=h_{ji}$ such that
$$ w_i=\sum_{j=1}^p h_{ij} v_j $$Do not confuse with Cartan formula.
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Author of the notes: Antonio J. Pan-Collantes
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