@article{Chen2024, 
author = {Yinlan Chen and Wenting Duan},
title = {The Hermitian solution to a matrix inequality under linear constraint},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {20163-20172},
keywords = {matrix inequality, matrix equation, Hermitian solution, spectral decomposition, generalized singular value decomposition},
url = {https://www.sciopen.com/article/10.3934/math.2024982},
doi = {10.3934/math.2024982},
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.}
}