An analytical theory has been produced for describing the vector nature of the digital magnetic recording process in thin-film isotropic media. It is based upon assumptions on the way in which the magnetization follows the field during the recording process and shows, except for a scaling of their peak values, that the longitudinal and perpendicular components of magnetization behave, respectively, as if they were separately present in a longitudinal and perpendicular recording. The magnitudes of the longitudinal and perpendicular magnetization components are derived in particular cases.