The invention discloses a reciprocal radial field electric machine based on the soft magnetic attraction principle, characterized by a plurality of active elements organized as a bi-dimensional cylindrical machine matrix and fed sequentially by an external power converter in order to derive a motoring or generation effect. The machine is comprised of a fixed stator matrix featuring salient poles and electrical coils, and a mobile rotor matrix featuring salient poles. The machine works on the principle of time integration of the discrete actions performed by its active elements. The bi-dimensional matrix organization of the active elements and the algorithms of their activation in both motoring and generation modes are key features for the functional cohesion of the machine. The design of this machine is based on a unique digital modeling method developed by the inventors, using exclusively the matrix calculus adapted to cylindrical matrices.