Ranks and the least-norm of the general solution to a system of quaternion matrix equations

DOI10.1016/j.laa.2008.05.031zbMath1158.15010OpenAlexW2160914386MaRDI QIDQ1002265

Cheng-Kun Li, Qing-Wen Wang

Publication date: 25 February 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.2008.05.031

zbMATH Keywords

Moore-Penrose inverseminimal rankmaximal ranksystem of quaternion matrix equationslinear matrix expressionleast-norm

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) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (92)

The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix ⋮ On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation ⋮ The reflexive least squares solutions of the general coupled matrix equations with a submatrix constraint ⋮ Solutions to the linear transpose matrix equations and their application in control ⋮ The iterative solution of a class of tensor equations via Einstein product with a tensor inequality constraint ⋮ Extending the CGLS algorithm for least squares solutions of the generalized Sylvester-transpose matrix equations ⋮ Extreme Ranks of a Partial Banded Block Quaternion Matrix Expression Subject to Some Matrix Equations with Applications ⋮ Ranks of a constrained Hermitian matrix expression with applications ⋮ The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ Least squares solution of the linear operator equation ⋮ Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm ⋮ A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications ⋮ The general coupled matrix equations over generalized bisymmetric matrices ⋮ A real quaternion matrix equation with applications ⋮ The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations ⋮ Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations ⋮ Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix ⋮ A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations ⋮ Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations ⋮ Theη-bihermitian solution to a system of real quaternion matrix equations ⋮ Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ The solutions to linear matrix equations \(AX=B\), \(YA=D\) with \(k\)-involutory symmetries ⋮ 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 ⋮ Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Compact formula for skew-symmetric system of matrix equations ⋮ Cramer's rules of \(\eta \)-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations ⋮ 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 ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations ⋮ On solutions of the quaternion matrix equation \(AX=B\) and their applications in color image restoration ⋮ Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation ⋮ An efficient method for special least squares solution of the complex matrix equation \((AXB,CXD)=(E,F)\) ⋮ Inertias and ranks of some Hermitian matrix functions with applications ⋮ An iterative algorithm for the generalized reflexive solutions of the general coupled matrix equations ⋮ Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations ⋮ An iterative algorithm for periodic Sylvester matrix equations ⋮ An iterative algorithm to solve the generalized Sylvester tensor equations ⋮ Solvability of new constrained quaternion matrix approximation problems based on core-EP inverses ⋮ On extremal ranks and least squares solutions subject to a rank restriction ⋮ Ranks of the common solution to six quaternion matrix equations ⋮ The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation ⋮ Double parameter splitting (DPS) iteration method for solving complex symmetric linear systems ⋮ Characterization for the general solution to a system of matrix equations with quadruple variables ⋮ General theory of the higher-order quaternion linear difference equations via the complex adjoint matrix and the quaternion characteristic polynomial ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ A quick exponentiation algorithm for \(3\times 3\) block upper triangular matrices ⋮ On the generalized reflexive and anti-reflexive solutions to a system of matrix equations ⋮ An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices ⋮ The scaling conjugate gradient iterative method for two types of linear 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 ⋮ The (R, S)-symmetric least squares solutions of the general coupled matrix equations ⋮ A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ (\(R,S\))-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 reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations ⋮ L-structured quaternion matrices and quaternion linear matrix equations ⋮ An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations ⋮ On the solutions of two systems of quaternion matrix equations ⋮ The Common Solution of Some Matrix Equations ⋮ Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems ⋮ Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations ⋮ Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer's rule ⋮ An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies ⋮ Floquet theory for quaternion-valued differential equations ⋮ Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations ⋮ Least squares solution of the quaternion matrix equation with the least norm ⋮ 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 ⋮ The double-step scale splitting method for solving complex Sylvester matrix equation ⋮ A system of real quaternion matrix equations with applications ⋮ Convergence of an iterative method for solving Sylvester matrix equations over reflexive matrices ⋮ Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices ⋮ Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ Iterative methods to solve the generalized coupled Sylvester-conjugate matrix equations for obtaining the centrally symmetric (centrally antisymmetric) matrix solutions ⋮ Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations ⋮ Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation ⋮ Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations ⋮ Matrix form of the CGS method for solving general coupled matrix equations ⋮ The Solution Set to the Quaternion Matrix Equation $AX-\overline{X}B=0$

Cites Work

• The matrix equations \(AX=C\), \(XB=D\)
• Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix
• The spectral theorem in quaternions
• The maximal and minimal ranks of \(A - BXC\) with applications
• A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application
• The common solution to six quaternion matrix equations with applications
• Ranks of solutions of the linear matrix equation \(AX + YB = C\)
• \(P\)-(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 solvability of two linear matrix equations
• Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
• Ranks of Solutions of the Matrix Equation AXB = C
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Ranks and the least-norm of the general solution to a system of quaternion matrix equations