DOI10.1016/j.laa.2009.02.010zbMath1180.15019OpenAlexW1980549954MaRDI QIDQ1039739
Hai-Xia Chang, Qing-Wen Wang, Jacob W. van der Woude
Publication date: 23 November 2009
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2009.02.010
An efficient method for least-squares problem of the quaternion matrix equationX-AX̂B=C ⋮
Hermitian solutions to the system of operator equations T_iX=U_i. ⋮
Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations ⋮
A general method for solving linear matrix equations of elliptic biquaternions with applications ⋮
Extreme Ranks of a Partial Banded Block Quaternion Matrix Expression Subject to Some Matrix Equations with Applications ⋮
An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\) ⋮
Solving optimization problems on Hermitian matrix functions with applications ⋮
Least squares solution of the linear operator equation ⋮
Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm ⋮
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 general solutions to some systems of matrix equations ⋮
The general coupled matrix equations over generalized bisymmetric matrices ⋮
Solutions to matrix equations \(X - AXB = CY + R\) and \(X - A\hat{X}B = CY + R\) ⋮
A finite iterative algorithm for the general discrete-time periodic Sylvester matrix equations ⋮
A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations ⋮
Determinantal representations of solutions to systems of quaternion matrix equations ⋮
Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications ⋮
Common solutions to some operator equations over HilbertC*–modules and applications ⋮
Theη-bihermitian solution to a system of real quaternion matrix equations ⋮
Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation ⋮
Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations ⋮
On the general solutions to some systems of quaternion matrix equations ⋮
The extremal ranks and inertias of matrix expressions with respect to generalized reflexive and anti-reflexive matrices with applications ⋮
An efficient algorithm for solving general coupled matrix equations and its application ⋮
Minimal ranks of some quaternion matrix expressions with applications ⋮
A system of matrix equations and its applications ⋮
Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮
Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation ⋮
Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations ⋮
Adaptive parameter alternating direction algorithm for centrosymmetric solutions of a class of generalized coupled Sylvester-transpose matrix equations ⋮
The consistency and the exact solutions to a system of matrix equations ⋮
A system of coupled quaternion matrix equations with seven unknowns and its applications ⋮
A finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations by using the linear operators ⋮
Centrohermitian and skew-centrohermitian solutions to the minimum residual and matrix nearness problems of the quaternion matrix equation \((AXB,DXE) = (C,F)\) ⋮
The solution of a generalized Sylvester quaternion matrix equation and its application ⋮
Common solutions to the matrix equations \(AX=B\) and \(XC=D\) on a subspace ⋮
The general solution to a system of linear coupled quaternion matrix equations with an application ⋮
A numerical method of structure-preserving model updating problem and its perturbation theory ⋮
An expression of the general common least-squares solution to a pair of matrix equations with applications ⋮
\( \eta \)-Hermitian solution to a system of quaternion matrix equations ⋮
An iterative algorithm for periodic Sylvester matrix equations ⋮
The generalized bisymmetric (bi-skew-symmetric) solutions of a class of matrix equations and its least squares problem ⋮
Systems of coupled generalized Sylvester matrix equations ⋮
Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving \(\phi\)-skew-Hermicity ⋮
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 ⋮
The Hermitian solution of \(A X A^* = B\) subject to \(CXC^{*} \geq D\) ⋮
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 ⋮
Optimization of a nonlinear Hermitian matrix expression with application ⋮
A system of quaternary coupled Sylvester-type real quaternion matrix equations ⋮
Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮
On the generalized reflexive and anti-reflexive solutions to a system of matrix equations ⋮
Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating ⋮
An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications ⋮
(\(R,S\))-conjugate solution to a pair of linear matrix equations ⋮
Matrix equations over \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices ⋮
Solutions to optimization problems on ranks and inertias of a matrix function with applications ⋮
The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations ⋮
A quaternion matrix equation with two different restrictions ⋮
L-structured quaternion matrices and quaternion linear matrix equations ⋮
The least square solution with the least norm to a system of quaternion matrix equations ⋮
On the solutions of two systems of quaternion matrix equations ⋮
The Common Solution of Some Matrix Equations ⋮
On solutions of the generalized Stein quaternion matrix equation ⋮
Common nonnegative definite solutions of some classical matrix equations ⋮
Positive solutions to a system of adjointable operator equations over Hilbert \(C^*\)-modules ⋮
GENERAL Φ-HERMITIAN SOLUTION TO A SYSTEM OF QUATERNION MATRIX EQUATIONS ⋮
Finite iterative solutions to periodic Sylvester matrix equations ⋮
An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies ⋮
Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations ⋮
A QUATERNION MATRIX EQUATION INVOLVING Φ-HERMICITY ⋮
BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix ⋮
Decomposition for a quaternion tensor triplet with applications ⋮
Iterative algorithm for solving a class of quaternion matrix equation over the generalized \((P, Q)\)-reflexive matrices ⋮
Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices ⋮
Algebraic conditions for the solvability to some systems of matrix equations ⋮
Cramer's rule for a system of quaternion matrix equations with applications ⋮
Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm ⋮
Determinantal representations of solutions to systems of two-sided quaternion matrix equations ⋮
Some new results on a system of Sylvester-type quaternion matrix equations ⋮
Some quaternion matrix equations involving Φ-Hermicity ⋮
Solvability conditions for mixed sylvester equations in rings ⋮
Some matrix equations with applications†
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- Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
- New solvable conditions and a new expression of the general solution to a system of linear matrix equation over an arbitrary division ring
- The common solution to matrix equations over a regular ring with applications
- The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations
- Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
- Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations
- Geršgorin type theorems for quaternionic matrices
- Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices
- On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
- The generalized reflexive solution for a class of matrix equations \( (AX=B, XC=D)\)
- Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
- Ranks and the least-norm of the general solution to a system of quaternion matrix equations
- On the reducibility of centrosymmetric matices - applications in engineering problems
- The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
- Characterization and properties of matrices with generalized symmetry or skew symmetry.
- Symmetric centrosymmetric matrix-vector multiplication
- A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
- Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
- \(P\)-(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
- The reflexive solutions of the matrix equation \(AX B = C\)
- Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
- The general solution to a system of real quaternion matrix equations
- A system of four matrix equations over von Neumann regular rings and its applications
- A Spectral Characterization of Generalized Real Symmetric Centrosymmetric and Generalized Real Symmetric Skew-Centrosymmetric Matrices
- Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
- Generalized Reflexive Matrices: Special Properties and Applications
- Right eigenvalue equation in quaternionic quantum mechanics
- Spectral Characterizations for Hermitian Centrosymmetric K-Matrices and Hermitian Skew-Centrosymmetric K-Matrices
- Characterization and Properties of (R,S)-Symmetric, (R,S)-Skew Symmetric, and (R,S)-Conjugate Matrices
- On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
- Best Approximate Solution of Matrix Equation AXB+CYD=E
- Quaternions and matrices of quaternions
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