On the construction of a decomposable linearization of nonregular polynomial matrices

The analysis of a homogeneous system of algebraic-differential equations is related to the algebraic structure of the polynomial matrix that describes the system. A decomposable pair containing this algebraic structure exists for the regular case. Extending the results to the nonregular case, we construct a decomposable pair containing information from the right minimal indices of the polynomial matrix, in addition to the information coming from its finite and infinite elementary divisors. Once again a ´decomposable linearization´ is introduced.