Serre's Reduction of Linear Functional Systems

Serre's reduction aims at reducing the number of unknowns and equations of a linear functional system. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help solving the linear functional system. The purpose of this paper is to present a constructive approach to Serre's reduction for determined and underdetermined linear functional systems.