二元多项式矩阵Smith型等价问题

On the Equivalence to the Smith Form of Bivariate Polynomial Matrices

二维系统等价是多维系统研究中的重要问题,它常被转化为二元多项式矩阵的等价问题来研究。二元多项式矩阵与其Smith型等价是矩阵等价研究中的重要问题。本文主要研究几类二元多项式矩阵与其Smith型等价问题,给出二元多项式矩阵约化到其Smith型的一些结果和判别条件。这些条件可以通过计算矩阵既约子式的约化Gröbner基进行检验。

The equivalence of two-dimensional systems is an important content of multidimensional systems,which is usually rep⁃resented by the bivariate polynomial matrices.Reducing a matrix to its Smith form is a very important study in the equivalence of matrices.In this paper we mainly investigate the reduction of several kinds of bivariate polynomial matrices to their Smith forms.Some new results and criteria are presented.These criteria can be verified easily by computing the Gröbner basis of the associated ideals.