State Space Decomposition into Cyclic Subspaces and Transformation to the Jordan Form

A new simple algorithm for the decomposition of the state space of a dynamical system into the minimal number of cyclic subspaces is proposed. This algorithm allows to perform the transformation to the Jordan form using the same fast techniques already known for systems with a cyclic dynamical matrix. The proposed algorithm does not introduce any assumption on the considered system and gives also, as a byproduct, the minimal and characteristic polynomials of the system dynamical matrix.