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.
Citation: Yinlan Chen, Wenting Duan. The Hermitian solution to a matrix inequality under linear constraint[J]. AIMS Mathematics, 2024, 9(8): 20163-20172. doi: 10.3934/math.2024982
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.
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Yinlan Chen, Wenting Duan. The Hermitian solution to a matrix inequality under linear constraint[J]. AIMS Mathematics, 2024, 9(8): 20163-20172. doi: 10.3934/math.2024982
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