Catadioptric cameras are a popular type of omnidirectional imaging system. Their imaging and multi-view geometry has been exten- sively studied; epipolar geometry for instance, is geometrically speaking, well understood. However, the existence of a bilinear matching constraint and an associated fundamental matrix, has so far only been shown for the special case of para-catadioptric cameras (consisting of a paraboloidal mirror and an orthographic camera). The main goal of this work is to obtain such results for all central catadioptric cameras. Our main result is to show the existence of a general 15x15 fundamental matrix. This is based on and completed by a number of other results, e.g. the formulation of general catadioptric projection matrices and plane homographies.