Further results on equivalence of multivariate polynomial matrices

TL;DR

This paper explores the equivalence of certain multivariate polynomial matrices, extending a theorem by Vaserstein, and proves their equivalence to Smith forms using a generalized global-local theorem.

Contribution

It generalizes Vaserstein's global-local theorem and establishes the equivalence of specific polynomial matrices to their Smith forms.

Findings

Matrices are equivalent to their Smith forms

Generalization of Vaserstein's theorem

New conditions for matrix equivalence

Abstract

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these matrices are equivalent to their Smith forms by the generalized global-local theorem.