Equivalent of Multivariate Polynomial Matrix

Abstract: The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices into Smith normal form has not been fully solved. This article investigates the Smith normal form of quasi weakly linear multivariate polynomial matrices. Breaking through previous limitations, providing sufficient and necessary conditions.