The Tutte matrix is a mathematical construct used in graph theory, particularly for analyzing the properties of graphs. It is a square matrix associated with a graph, where the entries are determined by the edges and vertices of the graph. The matrix helps in determining whether a graph is bipartite and can also be used to find perfect matchings. In the context of graph theory, the Tutte matrix is named after the mathematician W. T. Tutte, who made significant contributions to the field. The matrix is particularly useful in studying the existence of matchings in bipartite graphs and has applications in various areas, including network theory and combinatorial optimization.