New results on the equivalence of bivariate polynomial matrices

*Xiaopeng Zheng (中国科学院数学与系统科学研究院)
Dong Lu (北京航空航天大学)
Dingkang Wang (中国科学院数学与系统科学研究院)
Fanghui Xiao (湖南师范大学)

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, we 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. The results presented in the paper are also true for the non-square case.