Hermitian‐type generalized singular value decomposition with applications

DOI10.1002/nla.1825zbMath1289.65108OpenAlexW2170774163MaRDI QIDQ5397303

Yongge Tian, Yong Hui Liu

Publication date: 19 February 2014

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.1825

zbMATH Keywords

rankHermitian matrixmatrix equationgeneralized singular value decompositioneigenvalue decompositionsHermitian and nonnegative definite solutions

Mathematics Subject Classification ID

Related Items (4)

Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions ⋮ Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm ⋮ A survey on rank and inertia optimization problems of the matrix-valued function \(A+BXB^\ast\) ⋮ Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices

Cites Work

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• Equalities and inequalities for inertias of Hermitian matrices with applications
• Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\)
• The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(AXA^{\ast}=B\)
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• A note on the existence of the hyperbolic singular value decomposition
• Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function
• Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications
• A simultaneous decomposition of a matrix triplet with applications
• The Restricted Singular Value Decomposition of Matrix Triplets
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• More on extremal ranks of the matrix expressions A  − BX  ± X ^* B ^* with statistical applications
• On rank-constrained Hermitian nonnegative-definite least squares solutions to the matrix equationAXA^H=B
• Towards a Generalized Singular Value Decomposition
• The Restricted Singular Value Decomposition: Properties and Applications
• Generalizing the Singular Value Decomposition
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications

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