论文标题
关于一类多元多项式矩阵的分解和等效问题的新评论
New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial Matrices
论文作者
论文摘要
本文涉及多元多项式矩阵的分解和等效问题。我们提供了一些针对一类多个多项式矩阵的矩阵因素化的新标准，并获得了等效性多项式基质和对角线矩阵的必要条件。基于新标准的建设性证明，我们给出了一种分解算法并证明了分解的独特性。我们在枫树上实施了算法，并给出了两个说明性示例以显示算法的有效性。
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain a necessary and sufficient condition for the equivalence of a square polynomial matrix and a diagonal matrix. Based on the constructive proof of the new criteria, we give a factorization algorithm and prove the uniqueness of the factorization. We implement the algorithm on Maple, and two illustrative examples are given to show the effectiveness of the algorithm.
