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

页码：20163 / 20172

页数：10

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