Represent of multilinear map

Question

Let $V_1,V_2$ be vector space and $\{e_i\},\{\overline e_i\}$ are basis respectively. $\forall ~l\in L(V_1,V_2; F)$ ,why $l$ can be represented as $$ l=\sum\limits_{ij} a_{ij} \omega^i\otimes \overline\omega^j ~~~~~~~? $$ $a_{ij}=l(e_i,\overline e_j)$ and $\{\omega^i\},\{\overline\omega^i\}$ is dual basis of $\{e_i\},\{\overline e_i\}$ . $L(V_1,V_2; F)$ is 2 multilinear function space .