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Research Article | Open Access

The Hermitian solution to a matrix inequality under linear constraint

Yinlan Chen( ), Wenting Duan
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China
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Abstract

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.

Keywords

matrix inequalitymatrix equationHermitian solutionspectral decompositiongeneralized singular value decomposition
CLC number: 15A24, 15A57

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 20163-20172
DOI: 10.3934/math.2024982

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Cite this article:
Chen Y, Duan W. The Hermitian solution to a matrix inequality under linear constraint. AIMS Mathematics, 2024, 9(8): 20163-20172. https://doi.org/10.3934/math.2024982

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Received: 29 April 2024
Revised: 31 May 2024
Accepted: 12 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)