New Results on the Equivalence of Bivariate Polynomial Matrices

This paper investigates the equivalence problem of bivariate polynomial matrices.A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is proposed.Meanwhile,the authors present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms,and an example is given to illustrate the effectiveness of the algorithm.In addition,the authors generalize the main result to the non-square case.