The common solution to six quaternion matrix equations with applications
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Publication:2425976
DOI10.1016/j.amc.2007.08.091zbMath1141.15016OpenAlexW2155989964MaRDI QIDQ2425976
Qing-Wen Wang, Hai-Xia Chang, Qun Ning
Publication date: 17 April 2008
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2007.08.091
generalized inversesymmetric solutionquaternion fieldpersymmetric solutioncentrosymmetric solutionsquaternion matrix solutionsystem of six quaternion matrix equations
Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)
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Cites Work
- 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
- 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
- A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
- Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing
- Almost non-interacting control by measurement feedback
- The spectral theorem in quaternions
- One-sided complements and solutions of the equation \(aXb=c\) in semirings
- A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
- Investigation and solution of matrix equations over associative rings
- Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application
- \(P\)-(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
- 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 common solution to a pair of linear matrix equations over a principal ideal domain
- Right eigenvalue equation in quaternionic quantum mechanics
- Hypercomplex correlation techniques for vector images
- Littlewood's algorithm and quaternion matrices
- Quaternions and matrices of quaternions
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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