Surjective linear transformations of tropical matrices preserving transitive closures

被引:0
作者
Deng, Weina [1 ,2 ,4 ]
Yu, Baomin [3 ]
机构
[1] Huanghuai Univ, Sch Math & Stat, Zhumadian, Henan, Peoples R China
[2] Northwest Univ, Sch Math, Xian, Shaanxi, Peoples R China
[3] Weinan Normal Univ, Sch Math & Stat, Weinan, Shaanxi, Peoples R China
[4] Huanghuai Univ, Sch Math & Stat, Zhumadian 463000, Henan, Peoples R China
基金
中国国家自然科学基金;
关键词
Linear preserver; transitive closure; tropical matrix; tropical semiring; IDEMPOTENT MATRICES; OPERATORS; MAPS;
D O I
10.1080/00927872.2022.2153254
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we characterize those surjective linear transformations of tropical matrices preserving the set of all weak transitive closures MnW and the set of all strong transitive closures MnS, respectively. We illustrate that there exist non-surjective linear transformations that preserve MnW or MnS. Also, we consider the strongly linear preservers of MnW and MnS, respectively.
引用
收藏
页码:2183 / 2198
页数:16
相关论文
共 20 条
  • [1] LINEAR-OPERATORS STRONGLY PRESERVING IDEMPOTENT MATRICES OVER SEMIRINGS
    BEASLEY, L
    PULLMAN, NJ
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 160 : 217 - 229
  • [2] LINEAR-OPERATORS PRESERVING IDEMPOTENT MATRICES OVER FIELDS
    BEASLEY, LB
    PULLMAN, NJ
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 146 : 7 - 20
  • [3] Beasley LB., 2005, J MATH SCI, V131, P5919
  • [4] On maps preserving square roots of idempotent and rank-one nilpotent matrices
    Borisov, Nikita
    Julius, Hayden
    Sikora, Martha
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (06)
  • [5] Butkovic P, 2010, SPRINGER MONOGR MATH, P259, DOI 10.1007/978-1-84996-299-5_11
  • [6] On maps preserving products equal to a diagonalizable matrix
    Catalano, Louisa
    Julius, Hayden
    [J]. COMMUNICATIONS IN ALGEBRA, 2021, 49 (10) : 4334 - 4344
  • [7] Linear bijective maps preserving fixed values of products of matrices at fixed vectors
    Costara, Constantin
    [J]. COMMUNICATIONS IN ALGEBRA, 2022, 50 (03) : 920 - 926
  • [8] Linear preservers for matrices over a class of semirings
    Deng, Weina
    Ren, Miaomiao
    Yu, Baomin
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (21) : 6830 - 6845
  • [9] Gondran M., 1984, ANN DISCRETE MATH, V95, P147, DOI DOI 10.1016/S0304-0208(08)72960-8
  • [10] Linear transformations of tropical matrices preserving the cyclicity index
    Guterman, Alexander
    Kreines, Elena
    Thomassen, Carsten
    [J]. SPECIAL MATRICES, 2021, 9 (01): : 112 - 118