On rank-constrained Hermitian nonnegative-definite least squares solutions to the matrix equationAXAH=B

DOI10.1080/00207160701458344zbMath1129.15012OpenAlexW2037233910MaRDI QIDQ3595059

Musheng Wei, Qian Wang

Publication date: 10 August 2007

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701458344

zbMATH Keywords

rankmatrix equationrank-constrainedHermitian nonnegative-definite matricesrank-\(p\) Hermitian nonnegative-definite least squares solutions

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Inverse problems in linear algebra (15A29) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (23)

The minimal rank of \(A - BX\) with respect to Hermitian matrix ⋮ A simultaneous decomposition of a matrix triplet with applications ⋮ The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint ⋮ Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications ⋮ On least squares solutions subject to a rank restriction ⋮ A novel method for a class of structured low-rank minimizations with equality constraint ⋮ Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm ⋮ The real and complex Hermitian solutions to a system of quaternion matrix equations with applications ⋮ On extremal ranks and least squares solutions subject to a rank restriction ⋮ Common Hermitian least squares solutions of matrix equations \(A_1XA^*_1=B_1\) and \(A_2XA^*_2=B_2\) subject to inequality restrictions ⋮ Extremal ranks of some nonlinear matrix expressions with applications ⋮ Effective implementation to reduce execution time of a low-rank matrix approximation problem ⋮ Hermitian‐type generalized singular value decomposition with applications ⋮ Weighted steepest descent method for solving matrix equations ⋮ Accelerated method for optimization over density matrices in quantum state estimation ⋮ Numerical methods for solving some matrix feasibility problems ⋮ Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices ⋮ Perturbation analysis for the (skew) Hermitian matrix least squares problem \(AXA^H=B\) ⋮ Minimum rank Hermitian solution to the matrix approximation problem in the spectral norm and its application ⋮ Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius norm ⋮ Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation ⋮ Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\) ⋮ Minimum rank (skew) Hermitian solutions to the matrix approximation problem in the spectral norm

Cites Work

• 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
• Linear matrix equations from an inverse problem of vibration theory
• The variation of the spectrum of a normal matrix
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
• Matrix theory. Basic results and techniques

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