The Hermitian solution to a matrix inequality under linear constraint

In this paper, the necessary and sufficient conditions under which the matrix inequality $ C^*XC\geq 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 matr...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 8; pp. 20163 - 20172
Main Authors Chen, Yinlan, Duan, Wenting
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
generalized singular value decomposition
hermitian solution
matrix equation
matrix inequality
spectral decomposition
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Summary:In this paper, the necessary and sufficient conditions under which the matrix inequality $ C^*XC\geq 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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024982