Geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities (shear, vorticity, expansion) of the congruence of the vector field generating the collineation. It is shown that the generic form of a collineation is Lξgab = 2ψgab + Hab where Hab is a traceless symmetric tensor. A general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed.