New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices. (March 2023)

• Record Type: Journal Article
• Authors: Lu, Dong; Wang, Dingkang; Xiao, Fanghui
• Is Part Of: Journal of symbolic computation. Volume 115(2023)
• Page Start: 266
• Page End: 284
• Publication Date: 2023-03
• Subjects: Multivariate polynomial matrices -- Matrix factorization -- Matrix equivalence -- Column reduced minors -- Gröbner basis; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.07.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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.