In this paper we theoretically derive for the first time a matrix formalism for a coupled dual-core fiber optical parametric amplifier (FOPA). One of the most advantageous properties of this degenerate pump FOPA is the spectrally flat gain obtained when certain design parameters are met. This flat gain is obtained either in phase-sensitive (PS) or phase-insensitive (PI) operation of the dual-core FOPA. Properties such as maximum and minimum PS gain, along with maximum bandwidth and difference between maximum PS and PI gain are also investigated.