The Hermitian solution of \(A X A^* = B\) subject to \(CXC^{*} \geq D\)

DOI10.1016/j.amc.2015.08.102zbMath1410.15031OpenAlexW1517823104MaRDI QIDQ670854

Xifu Liu

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.102

zbMATH Keywords

linear matrix inequalityLöwner partial orderinglinear matrix equationHermitian solution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Linear inequalities of matrices (15A39) Matrix equations and identities (15A24)

Related Items (2)

Solvability of the matrix inequality ⋮ Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices

Cites Work

• A Hermitian least squares solution of the matrix equation \(AXB=C\) subject to inequality restrictions
• Max-min problems on the ranks and inertias of the matrix expressions \(A - BXC \pm (BXC)^{\ast}\) with applications
• An expression of the general common least-squares solution to a pair of matrix equations with applications
• Common Hermitian least squares solutions of matrix equations \(A_1XA^*_1=B_1\) and \(A_2XA^*_2=B_2\) subject to inequality restrictions
• A system of real quaternion matrix equations with applications
• The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics
• Solving the matrix inequality AXB + (AXB)^* ⩾ C
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations

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