The reflexive re-nonnegative definite solution to a quaternion matrix equation

被引：0
|
作者：
Wang, Qing-Wen [1 ]
Zhang, Fei [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2008年 / 17卷
关键词：
quaternion matrix equation; reflexive matrix; re-nonnegative definite matrix; reflexive re-nonnegative definite matrix;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper a necessary and sufficient condition is established for the existence of the reflexive re-nonnegative definite solution to the quaternion matrix equation AXA* = B, where * stands for conjugate transpose. The expression of such solution to the matrix equation is also givenfurthermore, a necessary and sufficient condition is derived for the existence of the general re- nonnegative definite solution to the quaternion matrix equation A(1)X(1)A(1)* + A(2)X(2)A(2)* = B. The representation of such solution to the matrix equation is given.
引用
收藏
页码：88 / 101
页数：14
相关论文
共 50 条
  • [21] 0 ITERATIVE ALGORITHM FOR THE GENERALIZED (P, Q)-REFLEXIVE SOLUTION OF A QUATERNION MATRIX EQUATION WITH j-CONJUGATE OF THE UNKNOWNS
    Li, N.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2015, 41 (01) : 1 - 22
  • [22] An Iterative Algorithm for the Generalized Reflexive Solution Group of a System of Quaternion Matrix Equations
    Jiang, Jing
    Li, Ning
    SYMMETRY-BASEL, 2022, 14 (04):
  • [23] The Subpositive Definite Solution of the Unified Algebraic Lyapunov Equation over Quaternion Field
    Huang Jing-Pin
    2011 30TH CHINESE CONTROL CONFERENCE (CCC), 2011, : 142 - 146
  • [24] The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
    Zhang, Xindong
    Feng, Xinlong
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2017, 18 (05) : 293 - 301
  • [25] Hermite Positive Definite Solution of a Class of Matrix Equation
    Liu, Panpan
    Zhang, Shugong
    Li, Qingchun
    CEIS 2011, 2011, 15
  • [26] Positive definite solution of a class of nonlinear matrix equation
    Duan, Xue-Feng
    Wang, Qing-Wen
    Li, Chun-Mei
    LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (06): : 839 - 852
  • [27] The Symmetric Ortho-symmetric Nonnegative Definite Solutions of the Matrix Equation AX = B
    Xiao, Qingfeng
    Zhang, Zhongzhi
    Hu, Xiyan
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 335 - 338
  • [28] The bi-Hermitian solution to a linear quaternion matrix equation
    Lin, Chun-Yan
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 173 - 176
  • [29] The congruence class solution to a real quaternion matrix equation with applications
    Zhang, Fei
    Wang, Qing-Wen
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 476 - 478
  • [30] The Solution of a Generalized Sylvester Quaternion Matrix Equation and Its Application
    Song, Guang-Jing
    Yu, Shaowen
    ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (03) : 2473 - 2492
12345