On factor left prime factorization problems for multivariate polynomial matrices

被引：4
|
作者：
Lu, Dong [1 ,2 ]
Wang, Dingkang [3 ,4 ]
Xiao, Fanghui [5 ]
机构：
[1] Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China
[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[5] Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China
来源：
MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING | 2021年 / 32卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Multivariate polynomial matrices; Matrix factorizations; Factor left prime (FLP); Column reduced minors; Free modules;
D O I：
10.1007/s11045-021-00768-x
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition for the existence of factor left prime factorizations of a class of multivariate polynomial matrices, and then design an algorithm to compute all factor left prime factorizations if they exist. We implement the algorithm on the computer algebra system Maple, and two examples are given to illustrate the effectiveness of the algorithm. The results presented in this paper are also true for the existence of factor right prime factorizations of multivariate polynomial matrices without full column rank.
引用
收藏
页码：975 / 992
页数：18
相关论文
共 50 条
  • [1] On factor left prime factorization problems for multivariate polynomial matrices
    Dong Lu
    Dingkang Wang
    Fanghui Xiao
    [J]. Multidimensional Systems and Signal Processing, 2021, 32 : 975 - 992
  • [2] On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
    LU Dong
    WANG Dingkang
    XIAO Fanghui
    [J]. Journal of Systems Science & Complexity, 2024, 37 (03) : 1295 - 1307
  • [3] On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
    Lu, Dong
    Wang, Dingkang
    Xiao, Fanghui
    [J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2024, 37 (03) : 1295 - 1307
  • [4] On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
    Dong Lu
    Dingkang Wang
    Fanghui Xiao
    [J]. Journal of Systems Science and Complexity, 2024, 37 : 1295 - 1307
  • [5] Multivariate Polynomial Matrices Factorization
    Li, Dongmei
    Liu, Jingwang
    [J]. PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 2, 2009, : 5 - 8
  • [6] On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices
    Jiancheng Guan
    Weiqing Li
    Baiyu Ouyang
    [J]. Journal of Systems Science and Complexity, 2018, 31 : 1647 - 1658
  • [7] On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices
    GUAN Jiancheng
    LI Weiqing
    OUYANG Baiyu
    [J]. Journal of Systems Science & Complexity, 2018, 31 (06) : 1647 - 1658
  • [8] On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices
    Guan Jiancheng
    Li Weiqing
    Ouyang Baiyu
    [J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2018, 31 (06) : 1647 - 1658
  • [9] On the equivalence and factorization of multivariate polynomial matrices
    Lin, Zhiping
    Boudellioua, M. S.
    Xu, Li
    [J]. 2006 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOLS 1-11, PROCEEDINGS, 2006, : 4911 - +
  • [10] New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices
    Lu, Dong
    Wang, Dingkang
    Xiao, Fanghui
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2023, 115 : 266 - 284
12345