A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications
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Publication:2904690
DOI10.1080/00927872.2011.562269zbMath1252.15014OpenAlexW2118859646MaRDI QIDQ2904690
Jacob W. van der Woude, Xia Zhang, Qing-Wen Wang
Publication date: 23 August 2012
Published in: Communications in Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00927872.2011.562269
Factorization of matrices (15A23) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03) Canonical forms, reductions, classification (15A21) Skew fields, division rings (12E15) Matrix pencils (15A22)
Related Items (13)
The general solutions to some systems of matrix equations ⋮ A system of matrix equations and its applications ⋮ Centrohermitian and skew-centrohermitian solutions to the minimum residual and matrix nearness problems of the quaternion matrix equation \((AXB,DXE) = (C,F)\) ⋮ A structure-preserving algorithm for the quaternion Cholesky decomposition ⋮ A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations ⋮ Simultaneous decomposition of quaternion matrices involving \(\eta\)-Hermicity with applications ⋮ Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore-Penrose inverse ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating ⋮ Solutions to optimization problems on ranks and inertias of a matrix function with applications ⋮ A quaternion matrix equation with two different restrictions ⋮ Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm
Cites Work
- Unnamed Item
- Unnamed Item
- Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
- Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices
- Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations
- An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
- Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
- Holomorphic curvature of complex Finsler submanifolds
- An iterative algorithm for the least squares bisymmetric solutions of the matrix equations \(A_{1}XB_{1}=C_{1},A_{2}XB_{2}=C_{2}\)
- Ranks and the least-norm of the general solution to a system of quaternion matrix equations
- On consistency, natural restrictions and estimability under classical and extended growth curve models
- A system of real quaternion matrix equations with applications
- Almost non-interacting control by measurement feedback
- Vandermonde and Wronskian matrices over division rings
- On matrix equivalence and matrix equations
- Semisimilarity for matrices over a division ring
- Roth's theorems and decomposition of modules
- Matrix equivalence and isomorphism of modules
- On a variational formulation of the QSVD and the RSVD
- A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
- Quivers and matrix equations
- A finite iterative method for solving a pair of linear matrix equations \((AXB,CXD)=(E,F)\)
- An iterative algorithm for solving a pair of matrix equations \(AYB=E\), \(CYD=F\) over generalized centro-symmetric matrices
- Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
- The general solution to a system of real quaternion matrix equations
- Maps on idempotent matrices over division rings
- The similarity reduction of matrices over a skew field
- A system of four matrix equations over von Neumann regular rings and its applications
- The solvability of two linear matrix equations
- Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications
- Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
- Towards a Generalized Singular Value Decomposition
- Generalizing the Singular Value Decomposition
- The Real Solutions to a System of Quaternion Matrix Equations with Applications
- On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
- Some Theorems On Matrices With Real Quaternion Elements
- A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications
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