The smith form of a multivariate polynomial matrix over an arbitrary coefficient field
Dongmei Li, Jinwang Liu, Delin Chu
Abstract
The equivalence of multidimensional systems is closely related to the equivalence of multivariate polynomial matrices, for which the Smith form plays an important role. In this paper we study multivariate polynomial matrices with their entries in the polynomial ring K[z1,z2,…,zn], where K is an arbitrary field. We derive some new conditions on reducing these matrices to their Smith forms. These conditions can be verified by computing the reduced Gröbner bases of the associated ideals.
Topics & Concepts
MathematicsPolynomial matrixMatrix polynomialPolynomialMultivariate statisticsEquivalence (formal languages)Polynomial ringStable polynomialField (mathematics)Pure mathematicsMatrix (chemical analysis)Characteristic polynomialCombinatoricsDiscrete mathematicsAlgebra over a fieldAlternating polynomialMathematical analysisStatisticsMaterials scienceComposite materialPolynomial and algebraic computationCoding theory and cryptographyAdvanced Differential Equations and Dynamical Systems