A Tutte matrix is a special type of matrix used in graph theory, particularly in the study of perfect matchings in bipartite graphs. It is constructed from the edges of a graph, where the entries represent the presence or absence of edges between vertices. The determinant of a Tutte matrix can provide important information about the number of matchings in the graph. Tutte matrices are named after the mathematician W. T. Tutte, who made significant contributions to combinatorial mathematics. They are particularly useful in determining whether a graph has a perfect matching, which is a set of edges that covers every vertex exactly once.