The general Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(GXG^{\ast} + HY H^{\ast}=C\)

DOI10.1007/BF02936098zbMath1042.15010OpenAlexW1992775510MaRDI QIDQ1428984

Xian Zhang

Publication date: 29 March 2004

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

Full work available at URL: https://doi.org/10.1007/bf02936098

zbMATH Keywords

singular value decompositionMoore-Penrose inversematrix equationHermitian nonnegative-definite solutionequivalent decompositionHermitian positive-definite solution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Linear equations (linear algebraic aspects) (15A06)

Related Items

A simultaneous decomposition of a matrix triplet with applications ⋮ Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation ⋮ Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮ The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation ⋮ The solvability conditions for inverse problems of anti-symmetric ortho-symmetric matrices ⋮ The matrix nearness problem associated with the quaternion matrix equation \(AXA^H+BYB^H=C\) ⋮ Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications

Cites Work

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• On solutions of matrix equation \(AXB+CYD=F\)
• The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(AXA^{\ast}=B\)
• Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
• Full-column rank solutions of the matrix equation \(AV\)=\(EVJ\)
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations

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