Evolution matrix in a coherence vector formulation for quantum Markovian master equations of N-level systems

Quantum Markovian master equation in N dimensions are systematically transformed into vector form by using the Lie algebra of the special unitary group SU(N). Density operators are represented through coherence vectors and the infinitesimal Kossakowski generator of completely positive quantum dynamical semigroups appears as a real evolution matrix that is not completely diagonalisable, in general. A complete classification of the spectrum of the latter and its Jordan canonical form, together with all types of associated stationary states, is given in detail. The results of this analysis are particularly suited for computations in practical applications.