Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field

被引：33
|
作者：
Song, Guang-Jing [1 ]
Wang, Qing-Wen [2 ,3 ]
Chang, Hai-Xia [4 ]
机构：
[1] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[3] Nanyang Technol Univ, Div Math Sci, Singapore 637371, Singapore
[4] Shanghai Finance Univ, Dept Appl Math, Shanghai 201209, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 06期
关键词：
Quaternion matrix; Cramer rule; Generalized inverse A(T.S)((2)); GENERALIZED INVERSE A(T; S)((2)); INCONSISTENT LINEAR-EQUATIONS; LEAST-NORM; REPRESENTATION; DETERMINANTS;
D O I：
10.1016/j.camwa.2011.01.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish the determinantal representations of the generalized inverses A(rT1.S1)((2)), A(lT2.S2)((2)), and A((T1.T2).(S1.S2))((2)) over the quaternion skew field by the theory of the column, and row determinants. In addition, we derive some generalized Cramer rules for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1576 / 1589
页数：14
相关论文
共 50 条
  • [31] Solvability Conditions and General Solution of a System of Matrix Equations Involving η-Skew-Hermitian Quaternion Matrices
    Rehman, Abdur
    Khan, Israr Ali
    Anjum, Rukhshanda
    Hussain, Iftikhar
    SYMMETRY-BASEL, 2021, 13 (10):
  • [32] Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
    Kyrchei, Ivan I.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2016, 2016
  • [33] An iterative solution to coupled quaternion matrix equations
    Song, Caiqin
    Chen, Guoliang
    Zhang, Xiangyun
    FILOMAT, 2012, 26 (04) : 809 - 826
  • [34] η-Hermitian Solution to a System of Quaternion Matrix Equations
    Liu, Xin
    He, Zhuo-Heng
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (06) : 4007 - 4027
  • [35] Solution to Several Split Quaternion Matrix Equations
    Liu, Xin
    Shi, Tong
    Zhang, Yang
    MATHEMATICS, 2024, 12 (11)
  • [36] The Solvability of a System of Quaternion Matrix Equations Involving φ-Skew-Hermicity
    He, Zhuo-Heng
    Zhang, Xiao-Na
    Zhao, Yun-Fan
    Yu, Shao-Wen
    SYMMETRY-BASEL, 2022, 14 (06):
  • [37] Hermite constant and Voronoi theory over a quaternion skew field
    Coulangeon, Renaud
    Watanabe, Takao
    OSAKA JOURNAL OF MATHEMATICS, 2006, 43 (03) : 517 - 556
  • [38] Least squares skew bisymmetric solution for a kind of quaternion matrix equation
    Yuan, Shifang
    Cao, Handong
    INTELLIGENT STRUCTURE AND VIBRATION CONTROL, PTS 1 AND 2, 2011, 50-51 : 190 - 194
  • [39] Quadratic Equations Over Matrix Skew Series
    Derevenskii, V. P.
    RUSSIAN MATHEMATICS, 2014, 58 (01) : 14 - 26
  • [40] Relative controllability of neutral delay differential equations on quaternion skew field
    Fu, Teng
    Wang, Jinrong
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2025, 142
12345