Abstract A new representation of the light field is proposed in this paper. It is shown that the wave theory of the light propagation can all be putted into a more convenient and more complete scheme of a matrix theory when the new representation is adopted. Some general fundamentals of this matrix theory are given, and the convergence of the action matrix is also proved in the general case.The expression of the light field proposed here involves the general characteristics of the monochromatic scalar wave field with only one propagation axis. It can also demonstrate explicitly the axial symmetry and the radial distribution features of this field on the plane which is perpendicular to the propagation axis. By virtue of this expression, some general laws of the distribution of the field on the plane, including the qualitative law of the distribution of the symmetries of the field along the radial direction, are obtained for the first time.