ABOUT THE DECOMPOSITION OF RATIONAL SERIES IN NONCOMMUTATIVE VARIABLES INTO SIMPLE SERIES

摘要

Similarly to the partial fraction decomposition of rational fractions, we provide an approach to the decomposition of rational series in non-commutative variables into simpler series. This decomposition consists in splitting the representation of the rational series into simpler representations. Finally, the problem appears as a joint block-diagonalization of several matrices. We present then an application of this decomposition to the integration of dynamical systems.