The Hermitian solution to a matrix inequality under linear constraint

被引：0
|
作者：
Chen, Yinlan [1 ]
Duan, Wenting [1 ]
机构：
[1] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Peoples R China
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 08期
关键词：
matrix inequality; matrix equation; Hermitian solution; spectral decomposition; generalized singular value decomposition; EQUATIONS;
D O I：
10.3934/math.2024982
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the necessary and sufficient conditions under which the matrix inequality C* XC >= D (> D) subject to the linear constraint A* XA = B is solvable are deduced by means of the spectral decompositions of some matrices and the generalized singular value decomposition of a matrix pair. An explicit expression of the general Hermitian solution is also provided. One numerical example demonstrates the effectiveness of the proposed method.
引用
收藏
页码：20163 / 20172
页数：10
相关论文
共 50 条
  • [41] Constraint-following control design for the position tracking of a permanent magnet linear motor with inequality constraints
    Chen, Xiaofei
    Zhao, Han
    Zhen, Shengchao
    MECHANICAL SCIENCES, 2022, 13 (01) : 297 - 310
  • [42] The R-conjugate Solution to a Pair of Linear Matrix Equations
    Chang, Haixia
    Wang, Qingwen
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 17 - 20
  • [43] (R, S)-conjugate solution to a pair of linear matrix equations
    Chang, Hai-Xia
    Wang, Qing-Wen
    Song, Guang-Jing
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (01) : 73 - 82
  • [44] The general common Hermitian nonnegative-definite solution to the matrix equations AXA* = B and CXC* = D
    Zhang, X
    LINEAR & MULTILINEAR ALGEBRA, 2004, 52 (01) : 49 - 60
  • [45] The Hermitian Positive Definite Solution of Nonlinear Matrix Equations X plus A*X-2A=I
    Zhao, Guangyuan
    PROCEEDINGS OF THE 2009 INTERNATIONAL CONFERENCE ON COMPUTER TECHNOLOGY AND DEVELOPMENT, VOL 2, 2009, : 561 - 563
  • [46] 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):
  • [47] MAXIMUM AND MINIMUM RANKS AND INERTIAS OF THE HERMITIAN PARTS OF THE LEAST RANK SOLUTION OF THE MATRIX EQUATION AXB = C
    Guerarra, Sihem
    NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2021, 11 (01): : 75 - 86
  • [48] The ?-(anti-)Hermitian solution to a constrained Sylvester-type generalized commutative quaternion matrix equation
    Chen, Xue-Ying
    Wang, Qing-Wen
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2023, 17 (03)
  • [49] Iterative methods for solving consistent or inconsistent matrix inequality AXB ≥ C with linear constraints
    Lei, Yuan
    Liao, An-Ping
    Qiao, Wen-Long
    APPLIED MATHEMATICAL MODELLING, 2015, 39 (14) : 4151 - 4163
  • [50] A converse of a matrix inequality
    Alzer, H
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 323 (1-3) : 195 - 199
12345