In graph theory, the Edmonds matrix of a balanced bipartite graph with sets of vertices and is defined by
where the x<sub>ij</sub> are indeterminates. One application of the Edmonds matrix of a bipartite graph is that the graph admits a perfect matching if and only if the polynomial det(A) in the x<sub>ij</sub> is not identically zero. Furthermore, the number of perfect matchings is equal to the number of monomials in the polynomial det(A), and is also equal to the permanent of . In addition, the rank of is equal to the maximum matching size of .
The Edmonds matrix is named after Jack Edmonds. The Tutte matrix is a generalisation to non-bipartite graphs.