A unified treatment for the restricted solutions of the matrix equation \(AXB=C\)

DOI10.3934/math.2020424zbMath1489.15026OpenAlexW3081188667MaRDI QIDQ2132224

Huiting Zhang, Hairui Zhang, Yongxin Yuan, Lina Liu, Jiao Xu

Publication date: 27 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2020424

zbMATH Keywords

matrix equationHermitian definite solutionleast-rank solution

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Hermitian, skew-Hermitian, and related matrices (15B57)

Cites Work

• Comments on ``The common Re-nnd and Re-pd solutions to the matrix equations \(AX=C\) and \(XB=D\)
• The re-nonnegative definite and re-positive definite solutions to the matrix equation \(AXB=D\)
• Nested splitting conjugate gradient method for matrix equation \(AXB=C\) and preconditioning
• On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation \(AXB=C\)
• Least squares solutions with special structure to the linear matrix equation \(AXB = C\)
• LSQR iterative common symmetric solutions to matrix equations \(AXB = E\) and \(CXD = F\)
• Generalized reflexive solutions of the matrix equation \(AXB=D\) and an associated optimal approximation problem
• The Re-positive definite solutions to the matrix inverse problem \(AX = B\)
• A note on Hurwitz stability of matrices
• Explicit solutions to the matrix inverse problem \(AX=B\)
• The minimal norm least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\)
• The Jacobi and Gauss-Seidel-type iteration methods for the matrix equation \(A X B = C\)
• The Re-nonnegative definite solutions to the matrix inverse problem \(AX=B\)
• Stationary splitting iterative methods for the matrix equation \(AXB=C\)
• Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications
• Relations between least-squares and least-rank solutions of the matrix equation \(AXB=C\)
• An alternative representation of the generalized inverse of partitioned matrices
• The Quadratic Eigenvalue Problem
• Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• The Equations A^TX\pm X^TA=B
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications
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