The skew-symmetric orthogonal solutions of the matrix equation \(AX=B\)

DOI10.1016/j.laa.2005.01.022zbMath1128.15301OpenAlexW1988961939MaRDI QIDQ556903

Chunjun Meng, Xi-Yan Hu, Lei Zhang

Publication date: 23 June 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.01.022

zbMATH Keywords

C-S decompositionLeading principal submatrixSkew-symmetric orthogonal matrixThe least-square solutionsThe matrix nearness problem

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

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Solving balanced Procrustes problem with some constraints by eigenvalue decomposition ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Numerical strategies for recursive least squares solutions to the matrix equation AX = B ⋮ Eigenvector-free solutions to \(AX = B\) with \(PX = XP\) and \(X^H = sX\) constraints ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ On solutions of the quaternion matrix equation \(AX=B\) and their applications in color image restoration ⋮ Constrained solutions of a system of matrix equations ⋮ Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices ⋮ Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators ⋮ A hybrid algorithm for solving minimization problem over (R,S)-symmetric matrices with the matrix inequality constraint ⋮ Least-squares solutions to the matrix equations \(AX = B\) and \(XC = D\) ⋮ Completion of symmetric orthogonal matrices and corresponding matrix equation problem ⋮ An efficient method for solving a matrix least squares problem over a matrix inequality constraint ⋮ Reflexive solution to a system of matrix equations ⋮ The structure of symmetric solutions of the matrix equation \(A X = B\) over a principal ideal domain ⋮ Least squares solutions to the equations \(AX = B, XC = D\) with some constraints ⋮ The \((P,Q)\) generalized reflexive and anti-reflexive solutions of the matrix equation \(AX=B\) ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ The *congruence class of the solutions of some matrix equations ⋮ The solution of the matrix equation \(AXB=D\) and The system of matrix equations \(AX=C\), \(XB=D\) with \(X^*X=I_p\) ⋮ The symmetric solutions of the matrix inequalityAX≥Bin least-squares sense

Cites Work

• The commutation matrix: Some properties and applications
• On the symmetric solutions of linear matrix equations
• On the symmetric solutions of a linear matrix equation
• The symmetric Procrustes problem
• Vector structures and solutions of linear matrix equations
• A generalized solution of the orthogonal Procrustes problem
• The Elimination Matrix: Some Lemmas and Applications
• The solvability conditions for the inverse eigenvalue problem of Hermitian-generalized Hamiltonian matrices
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