Bivariate Polynomial Matrix and Smith Form

被引：0
|
作者：
Zheng, Licui [1 ]
Wu, Tao [1 ]
Liu, Jinwang [1 ]
机构：
[1] Hunan Univ Sci & Technol, Dept Math & Comp Sci, Xiangtan 411201, Peoples R China
来源：
MATHEMATICS | 2024年 / 12卷 / 06期
基金：
中国国家自然科学基金;
关键词：
matrix equivalence; bivariate polynomial matrix; Smith form; EQUIVALENCE; FACTORIZATION; REDUCTION;
D O I：
10.3390/math12060815
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Matrix equivalence plays a pivotal role in multidimensional systems, which are typically represented by multivariate polynomial matrices. The Smith form of matrices is one of the important research topics in polynomial matrices. This article mainly investigates the Smith forms of several types of bivariate polynomial matrices and has successfully derived several necessary and sufficient conditions for matrix equivalence.
引用
收藏
页数：9
相关论文
共 50 条
  • [41] Sparse bivariate polynomial factorization
    Wu WenYuan
    Chen JingWei
    Feng Yong
    SCIENCE CHINA-MATHEMATICS, 2014, 57 (10) : 2123 - 2142
  • [42] Parallel algorithm for achieving the Smith normal form of an integer matrix
    Technische Universitaet Berlin, Berlin, Germany
    Parallel Comput, 10 (1399-1412):
  • [43] The Smith normal form of a specialized Giambelli-type matrix
    Gao, Alice L. L.
    Xie, Matthew H. Y.
    Yang, Arthur L. B.
    ADVANCES IN APPLIED MATHEMATICS, 2018, 92 : 1 - 16
  • [44] ON THE MINORS OF AN INCIDENCE MATRIX AND ITS SMITH NORMAL-FORM
    GROSSMAN, JW
    KULKARNI, DM
    SCHOCHETMAN, IE
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 218 : 213 - 224
  • [45] On efficient sparse integer matrix Smith normal form computations
    Dumas, JG
    Saunders, BD
    Villard, G
    JOURNAL OF SYMBOLIC COMPUTATION, 2001, 32 (1-2) : 71 - 99
  • [46] A parallel algorithm for achieving the Smith Normal Form of an integer matrix
    Neumann, I
    Wilhelmi, W
    PARALLEL COMPUTING, 1996, 22 (10) : 1399 - 1412
  • [47] To solve matrix equation ∑AiXBi = C by the Smith normal form
    Liping H.
    Applied Mathematics-A Journal of Chinese Universities, 2002, 17 (1) : 109 - 118
  • [48] An extension of the bivariate chromatic polynomial
    Averbouch, Ilia
    Godlin, Benny
    Makowsky, J. A.
    EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (01) : 1 - 17
  • [49] The bivariate Ising polynomial of a graph
    Andren, Daniel
    Markstrom, Klas
    DISCRETE APPLIED MATHEMATICS, 2009, 157 (11) : 2515 - 2524
  • [50] STRUCTURE AND SMITH-MACMILLAN FORM OF A RATIONAL MATRIX AT INFINITY
    VARDULAKIS, AIG
    LIMEBEER, DNJ
    KARCANIAS, N
    INTERNATIONAL JOURNAL OF CONTROL, 1982, 35 (04) : 701 - 725
12345