Edmonds matrix

For a bipartite graph $G(U,V,E)$ with sets of vertices $U=\{u_{1},u_{2},...,u_{n}\}$ and $V=\{v_{1},v_{2},...,v_{n}\}$. Then the Edmonds Matrix $\mathbf {A}$ of the bipartite graph is defined as:

$A_{ij}=\{{\begin{array}{ll}x_{ij}&(u_{i},v_{j})\in E\\0&(u_{i},v_{j})\notin E\end{array}}$