A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity

DOI10.1016/j.laa.2003.12.039zbMath1058.15015OpenAlexW2095771800MaRDI QIDQ1827477

Qing-Wen Wang

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.12.039

zbMATH Keywords

regular ringconsistencySylvester matrix equationlinear matrix equationsystem of matrix equationsinner inverse of a matrixreflexive inverse of a matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Linear equations (linear algebraic aspects) (15A06) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items

Generalized Matrix Nearness Problems ⋮ The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix ⋮ Hermitian solutions to the system of operator equations T_iX=U_i. ⋮ The general solution to a system of eight quaternion matrix equations with applications ⋮ Ranks of a constrained Hermitian matrix expression with applications ⋮ Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation ⋮ A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications ⋮ The least squares bisymmetric solution of quaternion matrix equation \(AXB = C\) ⋮ Rank equalities related to the generalized inverse \(A^{(2)}_{T,S}\) with applications ⋮ The general solutions to some systems of matrix equations ⋮ The general coupled matrix equations over generalized bisymmetric matrices ⋮ The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations ⋮ A simple method for solving matrix equations \(AXB = D\) and \(GXH = C\) ⋮ Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application ⋮ Algebraic conditions for the solvability of system of three linear equations in a ring ⋮ An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices ⋮ Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications ⋮ Common solutions to some operator equations over HilbertC^*–modules and applications ⋮ Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix ⋮ Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations ⋮ Minimal ranks of some quaternion matrix expressions with applications ⋮ The reflexive least squares solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2+\cdots +A_lX_lB_l=C\) with a submatrix constraint ⋮ An efficient algorithm for the submatrix constraint of the matrix equationA₁X₁B₁+A₂X₂B₂+···+A_lX_lB_l=C ⋮ The maximal and minimal ranks of a quaternion matrix expression with applications ⋮ On the Hermitian structures of the solution to a pair of matrix equations ⋮ Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations ⋮ The consistency and the general common solution to some quaternion matrix equations ⋮ Adaptive parameter alternating direction algorithm for centrosymmetric solutions of a class of generalized coupled Sylvester-transpose matrix equations ⋮ A new iterative algorithm for solving a class of matrix nearness problem ⋮ Cramer's rules of \(\eta \)-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations ⋮ The common solution to six quaternion matrix equations with applications ⋮ An iterative algorithm for the least squares generalized reflexive solutions of the matrix equations \(AXB = E\), \(CXD = F\) ⋮ The solution of a generalized Sylvester quaternion matrix equation and its application ⋮ The solvability and the exact solution of a system of real quaternion matrix equations ⋮ Factorization of Generalized Theta Functions Revisited ⋮ A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations ⋮ Finite iterative algorithms for solving generalized coupled Sylvester systems. I: One-sided and generalized coupled Sylvester matrix equations over generalized reflexive solutions ⋮ Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations ⋮ A simultaneous decomposition for seven matrices with applications ⋮ Iterative solutions to coupled Sylvester-transpose matrix equations ⋮ The estimation of eigenvalues of sum, difference, and tensor product of matrices over quaternion division algebra ⋮ Some considerations in relation to the matrix equation \(AXB = C\) ⋮ The iteration solution of matrix equation \(A X B = C\) subject to a linear matrix inequality constraint ⋮ On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity ⋮ Ranks of the common solution to six quaternion matrix equations ⋮ Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations ⋮ Constrained two-sided coupled Sylvester-type quaternion matrix equations ⋮ Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications ⋮ An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ Characterization for the general solution to a system of matrix equations with quadruple variables ⋮ \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations ⋮ Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications ⋮ A system of quaternary coupled Sylvester-type real quaternion matrix equations ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ The reflexive solutions of the matrix equation \(AX B = C\) ⋮ Cyclic and simultaneous iterative methods to matrix equations of the form \(A_iXB_i=F_i\) ⋮ On the generalized reflexive and anti-reflexive solutions to a system of matrix equations ⋮ An iterative algorithm for the generalized reflexive solutions of the generalized coupled Sylvester matrix equations ⋮ An iterative algorithm for the generalized reflexive solution of the matrix equations \(AXB = E, CXD = F\) ⋮ Distribution and estimation for eigenvalues of real quaternion matrices ⋮ Solutions of minus partial ordering equations over von Neumann regular rings ⋮ An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices ⋮ Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating ⋮ Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations ⋮ The general solution to a system of real quaternion matrix equations ⋮ An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications ⋮ Cramer's rule for the general solution to a restricted system of quaternion matrix equations ⋮ Iterative solution to a system of matrix equations ⋮ Matrix equations over \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices ⋮ The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations ⋮ A quaternion matrix equation with two different restrictions ⋮ Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2=C\) ⋮ Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices ⋮ Ranks and the least-norm of the general solution to a system of quaternion matrix equations ⋮ Reflexive solution to a system of matrix equations ⋮ Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations ⋮ Various solutions to reverse order law problems ⋮ Unnamed Item ⋮ AN ITERATIVE ALGORITHM FOR SOLVING A CLASS OF GENERALIZED COUPLED SYLVESTER-TRANSPOSE MATRIX EQUATIONS OVER BISYMMETRIC OR SKEW-ANTI-SYMMETRIC MATRICES ⋮ The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer's rule ⋮ The generalized bisymmetric solutions of the matrix equation \(A_{1} X_{1} B_{1} + A_{2} X_{2} B_{2} + \dots + A_{l} X_{l} B_{l} = C\) and its optimal approximation ⋮ Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations ⋮ Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications ⋮ The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E ⋮ BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations ⋮ A system of real quaternion matrix equations with applications ⋮ Convergence of an iterative method for solving Sylvester matrix equations over reflexive matrices ⋮ Algebraic conditions for the solvability to some systems of matrix equations ⋮ Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ Cramer's rule for a system of quaternion matrix equations with applications ⋮ Determinantal representations of solutions to systems of two-sided quaternion matrix equations ⋮ Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations ⋮ Some new results on a system of Sylvester-type quaternion matrix equations ⋮ A system of four matrix equations over von Neumann regular rings and its applications ⋮ Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations ⋮ Solvability conditions for mixed sylvester equations in rings ⋮ A System of Matrix Equations over the Quaternion Algebra with Applications ⋮ The Solution Set to the Quaternion Matrix Equation $AX-\overline{X}B=0$

Cites Work

• Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• Roth's theorems for sets of matrices
• Almost non-interacting control by measurement feedback
• Linear matrix equations: The module theoretic approach
• On matrix equivalence and matrix equations
• The matrix equation AXB+CYD=E
• Roth's theorems and decomposition of modules
• Matrix equivalence and isomorphism of modules
• Roth's theorems over commutative rings
• Roth's theorems for matrix equations with symmetry constraints
• The extension of Roth's theorem for matrix equations over a ring
• The generalized inverse of a sum with radical element: Applications
• Roth's removal rule revisited
• Roth's theorems for constant centroselfconjugate and centroskewselfconjugate solutions to systems of linear polynomial matrix equations over a finite dimensional central algebra
• Sylvester matrix equation for matrix pencils
• A common solution to a pair of linear matrix equations over a principal ideal domain
• The Equation $AXB + CYD = E$ over a Principal Ideal Domain
• Roth's Equivalence Problem in Unit Regular Rings
• Consistency of a pair of generalized Sylvester equations
• The matrix equationAXB+CYD=Eover a simple artinian ring
• The Maximal Regular Ideal of a Ring
• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity