The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations

DOI10.1216/RMJ-2010-40-3-825zbMath1198.15011MaRDI QIDQ983496

Masoud Hajarian, Mehdi Dehghan

Publication date: 23 July 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

matrix equationsreflexive matrixKronecker matrix productreflexive inverseanti-reflexive matrixgeneralized reflection matrixconditional inverse

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Linear equations (linear algebraic aspects) (15A06)

Related Items (31)

The reflexive least squares solutions of the general coupled matrix equations with a submatrix constraint ⋮ The general coupled matrix equations over generalized bisymmetric matrices ⋮ Norm estimates for function Lyapunov equations and applications ⋮ An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices ⋮ Generalized conjugate direction algorithm for solving the general coupled matrix equations over symmetric matrices ⋮ The Hermitian positive definite solution of the nonlinear matrix equation ⋮ An efficient algorithm for solving general coupled matrix equations and its application ⋮ Resolvents of functions of operators with Hilbert-Schmidt hermitian components ⋮ The maximal and minimal ranks of a quaternion matrix expression with applications ⋮ Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations ⋮ Triangular representations of functions of operators with Schatten–von Neumann Hermitian components ⋮ Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations ⋮ Least squares algorithm for an input nonlinear system with a dynamic subspace state space model ⋮ Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations ⋮ Norm estimates for functions of two non-commuting operators ⋮ The least squares Hermitian (anti)reflexive solution with the least norm to matrix equation \(A X B = C\) ⋮ On the generalized reflexive and anti-reflexive solutions to a system of matrix equations ⋮ An iterative algorithm for the generalized reflexive solution of the matrix equations \(AXB = E, CXD = F\) ⋮ An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices ⋮ Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice ⋮ An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications ⋮ A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation ⋮ Iterative solution to a system of matrix equations ⋮ Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2=C\) ⋮ Solving the general coupled and the periodic coupled matrix equations via the extended QMRCGSTAB algorithms ⋮ The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations ⋮ The anti-reflexive solutions for the matrix equation \( AV + BW = EVF + C \) ⋮ Norm estimates for solutions of polynomial operator equations ⋮ Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations ⋮ Finite algorithms for solving the coupled Sylvester-conjugate matrix equations over reflexive and Hermitian reflexive matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An efficient algorithm for solving general coupled matrix equations and its application
• Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2=C\)
• The general coupled matrix equations over generalized bisymmetric matrices
• The reflexive and anti-reflexive solutions of the matrix equation \(A^{H}XB=C\)
• On the symmetric solutions of linear matrix equations
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
• An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
• 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
• Symmetric solutions of linear matrix equations by matrix decompositions
• On solutions of matrix equation \(AXB+CYD=F\)
• The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
• Hierarchical gradient-based identification of multivariable discrete-time systems
• A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
• On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
• An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices
• The common solution to six quaternion matrix equations with applications
• The reflexive solutions of the matrix equation \(AX B = C\)
• Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• The general solution to a system of real quaternion matrix equations
• Iterative least-squares solutions of coupled sylvester matrix equations
• An iterative method for the least squares symmetric solution of the linear matrix equation \(AXB = C\)
• A system of four matrix equations over von Neumann regular rings and its applications
• On Iterative Solutions of General Coupled Matrix Equations
• ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD = E
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Some Results on Homogeneous Matrix Equations
• Generalized Reflexive Matrices: Special Properties and Applications
• The matrix equationAXB+CYD=Eover a simple artinian ring
• Hierarchical least squares identification methods for multivariable systems
• Gradient based iterative algorithms for solving a class of matrix equations
• Common Solutions for n Matrix Equations With Applications
• The Equations AX - YB = C and AX - XB = C in Matrices
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications

This page was built for publication: The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations