On the Hermitian solutions to a system of adjointable operator equations
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Publication:445851
DOI10.1016/j.laa.2012.05.012zbMath1276.47018OpenAlexW2129690072WikidataQ112882196 ScholiaQ112882196MaRDI QIDQ445851
Zhong-Cheng Wu, Qing-Wen Wang, F. O. Farid, Mohammad Sal Moslehian
Publication date: 27 August 2012
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2012.05.012
Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) (C^*)-modules (46L08) Equations involving linear operators, with operator unknowns (47A62)
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Cites Work
- Solutions to operator equations on Hilbert \(C^*\)-modules
- Particular formulae for the Moore-Penrose inverses of the partitioned bounded linear operators
- Common Hermitian and positive solutions to the adjointable operator equations \(AX = C\), \(XB = D\)
- Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators
- Common Hermitian solutions to some operator equations on Hilbert \(C^{*}\)-modules
- Moore--Penrose inverses of partitioned adjointable operators on Hilbert \(C^*\)-modules
- The symmetric solution of the matrix equations \(AX+YA=C, AXA^ t+BYB^ t=C\), and \((A^ tXA, B^ tXB)=(C,D)\)
- Generalized inverses and operator equations
- On solutions of matrix equation \(AXB+CYD=F\)
- Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
- Positive semi-definite matrices of adjointable operators on Hilbert \(C^{*}\)-modules
- Matrix Analysis
- Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
- Extremal Ranks of Some Symmetric Matrix Expressions with Applications
- Modules Over Operator Algebras
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