The left characteristic matrix equation (l.c.m.e.))of a delay system has been employed to develop a state feedback stabilization theory for delay systems. Analogously, the right characteristic matrix equation (r.c.m.e.) has led to the development of an observer theory for this class of systems. The characteristic matrix equation approach however only permits the relocation of integral multiples of n poles where n represents the system order. This restriction is removed in this work through a generalization of the l.c.m.e. and r.c.m.e. in a manner which permits the stabilization of an arbitrary but finite number of unstable modes. The resulting state feedback controller and state estimator permit the output feedback stabilization of the most general linear autonomous delay system under the minimal assumptions of spectral stabilizability and detectability.