An algebraic approach to Halls matching theorem abridged version

The purpose of this note is to present a proof of Hall's matching theorem (also called marriage theorem) which I have not encountered elsewhere in literature-what yet does not mean that it is necessarily new. We refer to Hall's theorem in the following form: Theorem 1 (Hall). Let n be a positive integer. Let be a bipartite graph whose set of vertices consists of n blue vertices B 1 ; B 2 Some notations used in this theorem require explanations: A bipartite graph is a (simple, non-directed) graph with each vertex colored either green or blue such that every edge of the graph connects a blue vertex and a green vertex.