Common Hermitian least squares solutions of matrix equations \(A_1XA^*_1=B_1\) and \(A_2XA^*_2=B_2\) subject to inequality restrictions

DOI10.1016/j.camwa.2011.07.029zbMath1231.15002OpenAlexW5095609MaRDI QIDQ660900

Ying Li, Fengxia Zhang, Jianli Zhao

Publication date: 5 February 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.07.029

zbMATH Keywords

rankgeneralized inverseinertiamatrix equationHermitian solutionsleast squares solutions

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (6)

An efficient method for least-squares problem of the quaternion matrix equationX-AX̂B=C ⋮ Solvability conditions and general solution for mixed Sylvester equations ⋮ The \(\{P, Q, k + 1 \}\)-reflexive solution to system of matrix equations \(A X = C\), \(X B = D\) ⋮ Real representation for solving reduced biquaternion matrix equations XF−AX=BY$$ XF- AX= BY $$ and XF−AX˜=BY$$ XF-A\tilde{X}= BY $$ ⋮ On the Hermitian \(R\)-conjugate solution of a system of matrix equations ⋮ The Hermitian solution of \(A X A^* = B\) subject to \(CXC^{*} \geq D\)

Cites Work

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• Equalities and inequalities for inertias of Hermitian matrices with applications
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• Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
• The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics
• Linear matrix equations from an inverse problem of vibration theory
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• On rank-constrained Hermitian nonnegative-definite least squares solutions to the matrix equationAXA^H=B
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications

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