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Communications in Algebra Volume 40, 2012 - Issue 7
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Original Articles

A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications

Qing-Wen Wang Department of Mathematics, Shanghai University, Shanghai, P.R. ChinaCorrespondence[email protected]
,
Xia Zhang Department of Mathematics, Shanghai University, Shanghai, P.R. China
&
J. W. van Der Woude Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
Pages 2309-2342 | Received 05 Aug 2010, Published online: 09 Jul 2012

Citations (14)

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Read on this site (2)

Zhuo-Heng He, Qing-Wen Wang & Yang Zhang. (2018) The complete equivalence canonical form of four matrices over an arbitrary division ring. Linear and Multilinear Algebra 66:1, pages 74-95.
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Zhuo-Heng He & Qing-Wen Wang. (2015) The general solutions to some systems of matrix equations. Linear and Multilinear Algebra 63:10, pages 2017-2032.
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Articles from other publishers (12)

Zhuo-Heng He, Jie Tian, Yun-Fan Zhao & Shao-Wen Yu. (2022) Consistency and General Solutions to Some Sylvester-like Quaternion Matrix Equations. Symmetry 14:7, pages 1350.
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Zhuo‐Heng He & Meng Wang. (2021) Solvability conditions and general solutions to some quaternion matrix equations. Mathematical Methods in the Applied Sciences 44:18, pages 14274-14291.
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Zhuo-Heng He & Meng Wang. (2021) A Quaternion Matrix Equation with Two Different Restrictions. Advances in Applied Clifford Algebras 31:2.
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Ivan Kyrchei. (2017) Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse. Applied Mathematics and Computation 309, pages 1-16.
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S. Şimşek, M. Sarduvan & H. Özdemir. (2016) Centrohermitian and Skew-Centrohermitian Solutions to the Minimum Residual and Matrix Nearness Problems of the Quaternion Matrix Equation $${(AXB,DXE) = (C,F)}$$ ( A X B , D X E ) = ( C , F ). Advances in Applied Clifford Algebras 27:3, pages 2201-2214.
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Zhuo-Heng He, Qing-Wen Wang & Yang Zhang. (2017) Simultaneous decomposition of quaternion matrices involving η-Hermicity with applications. Applied Mathematics and Computation 298, pages 13-35.
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Zhuoheng He & Qingwen Wang. (2017) A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations. Algebra Colloquium 24:01, pages 169-180.
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Wei-Ru Xu & Guo-Liang Chen. (2016) Inverse problems for -symmetric matrices in structural dynamic model updating . Computers & Mathematics with Applications 71:5, pages 1074-1088.
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Shi-Fang Yuan. (2014) Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation with the Least Norm . Journal of Applied Mathematics 2014, pages 1-9.
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Minghui Wang & Wenhao Ma. (2013) A structure-preserving algorithm for the quaternion Cholesky decomposition. Applied Mathematics and Computation 223, pages 354-361.
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QingWen Wang & ZhuoHeng He. (2013) A system of matrix equations and its applications. Science China Mathematics 56:9, pages 1795-1820.
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Zhuo-Heng He & Qing-Wen Wang. (2012) Solutions to optimization problems on ranks and inertias of a matrix function with applications. Applied Mathematics and Computation 219:6, pages 2989-3001.
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