Study of Polynomial and Matrix Fraction

Exploring the properties and applications of polynomials and polynomial matrices in linear systems

Abstract

This article illustrates how polynomials and polynomial matrices can be used to describelinear systems.  The focus is put on the transformation to and from the state-space equations, because it is a convenient way to introduce gradually the most important properties of polynomials and polynomial matrices, such as:  coprimeness, greatest common divisors, unimodularity, column- and row- reducedness, canonical Hermite or Popov forms.