The solutions to linear matrix equations \(AX=B\), \(YA=D\) with \(k\)-involutory symmetries

DOI10.1016/j.camwa.2017.02.012zbMath1370.15014OpenAlexW2592210636MaRDI QIDQ2402244

Wei-Ru Xu, Guo-Liang Chen

Publication date: 7 September 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.02.012

zbMATH Keywords

Moore-Penrose inverseleast squares solutionoptimal approximate solution\((R,S,\alpha,\mu)\)-symmetric matrix\((R,S,\mu)\)-symmetric matrix

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Cites Work

• The common \((P,Q)\) generalized reflexive and anti-reflexive solutions to \(AX=B\) and \(XC=D\)
• The common Re-nnd and Re-pd solutions to the matrix equations \(AX = C\) and \(XB = D\)
• Procrustes problems and associated approximation problems for matrices with \(k\)-involutory symmetries
• (\(R,S\))-conjugate solution to a pair of linear matrix equations
• The matrix equations \(AX=C\), \(XB=D\)
• Procrustes problems for (\(P,Q,\eta \))-reflexive matrices
• Structured Procrustes problem
• Characterization and properties of matrices with \(k\)-involutory symmetries
• Characterization and properties of matrices with \(k\)-involutory symmetries. II
• Least-squares solutions to the matrix equations \(AX = B\) and \(XC = D\)
• Ranks and the least-norm of the general solution to a system of quaternion matrix equations
• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry.
• Hermitian, Hermitian \(R\)-symmetric, and Hermitian \(R\)-skew symmetric Procrustes problems
• Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
• The Hermitian \(\{P,\mathrm k+1\}\)-(anti-)reflexive solutions of a linear matrix equation
• Pseudo-centrosymmetric matrices, with applications to counting perfect matchings
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• Least squares solutions to the equations \(AX = B, XC = D\) with some constraints
• An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies
• Procrustes problems and inverse eigenproblems for multilevel block α -circulants
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Circulative Matrices of Degree $\theta $
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Generalized Reflexive Matrices: Special Properties and Applications
• Mirrorsymmetric Matrices, Their Basic Properties, and an Application on Odd/Even-Mode Decomposition of Symmetric Multiconductor Transmission Lines
• Characterization and Properties of (R,S)-Symmetric, (R,S)-Skew Symmetric, and (R,S)-Conjugate Matrices
• Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction

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