Presents a general formulation for the realization of a linear state feedback system using output feedback. The proposed formulation can be applied to any linear state feedback design, provided that an observable output signal is available. We show that scalar output is sufficient to achieve the realization, even in the case of MIMO state feedback systems. In addition, the proposed output feedback formulation achieves the same closed-loop response as a state feedback system, even when a non-relaxed initial state is involved. We present both discrete-time and continuous-time formulations for the proposed method.