Action of a Polynomial Matrix on a Vector of Power Series
Ramamonjy Andriamifidisoa *
Department of Mathematics and Computer Science, Faculty of Sciences, University of Antananarivo, BOP 906, 101 Antananariivo, Madagascar, Higher Polytechnics Institute of Madagascar (ISPM), Ambatomaro, Antsobolo, 101 Antananarivo, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
The adjoint of the right multiplication of a row vector by a fixed polynomial matrix gives a left operation of the polynomial matrix on column vectors of power series. This explain the polynomial matrix and vector of powers series “multiplication”, used to define discrete linear dynamical systems, according to Willems and Oberst theory.
Keywords: Discrete linear dynamical system, behavior, polynomial operator in the shift, categories and functors, adjoint of a linear mapping, polynomial matrix.