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Linear and Multilinear Algebra Volume 62, 2014 - Issue 11
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Articles

The η-bihermitian solution to a system of real quaternion matrix equations

Zhuo-Heng HeDepartment of Mathematics, Shanghai University, Shanghai, P.R. China.
&
Qing-Wen WangDepartment of Mathematics, Shanghai University, Shanghai, P.R. China.Correspondence[email protected]
Pages 1509-1528 | Received 01 Jan 2013, Accepted 24 Aug 2013, Published online: 30 Sep 2013

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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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Salman Ahmadi-Asl & Fatemeh Panjeh Ali Beik. (2017) An efficient iterative algorithm for quaternionic least-squares problems over the generalized -(anti-)bi-Hermitian matrices. Linear and Multilinear Algebra 65:9, pages 1743-1769.
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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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Shi-Fang Yuan, An-Ping Liao & Peng Wang. (2015) Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F). Linear and Multilinear Algebra 63:9, pages 1849-1863.
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Articles from other publishers (30)

Long-Sheng Liu. (2023) The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application. Advances in Applied Clifford Algebras 33:4.
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Xi-Le Xu & Qing-Wen Wang. (2023) The consistency and the general common solution to some quaternion matrix equations. Annals of Functional Analysis 14:3.
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Abdur Rehman & Ivan I. Kyrchei. 2023. Inverse Problems - Recent Advances and Applications. Inverse Problems - Recent Advances and Applications.
Yang-Fan Xu, Qing-Wen Wang, Long-Sheng Liu & Mahmoud Saad Mehany. (2022) A constrained system of matrix equations. Computational and Applied Mathematics 41:4.
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Ruo-Nan Wang, Qing-Wen Wang & Long-Sheng Liu. (2022) Solving a System of Sylvester-like Quaternion Matrix Equations. Symmetry 14:5, pages 1056.
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Zhuo-Heng He, Carmeliza Navasca & Xiang-Xiang Wang. (2022) Decomposition for a Quaternion Tensor Triplet with Applications. Advances in Applied Clifford Algebras 32:1.
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Xiang Zhang. (2022) The η-Hermitian solutions to some systems of real quaternion matrix equations. Filomat 36:1, pages 315-330.
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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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Xin Liu & Zhuo-Heng He. (2020) $$\eta $$-Hermitian Solution to a System of Quaternion Matrix Equations. Bulletin of the Malaysian Mathematical Sciences Society 43:6, pages 4007-4027.
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Mengyan Xie & Qing-Wen Wang. (2020) Reducible solution to a quaternion tensor equation. Frontiers of Mathematics in China 15:5, pages 1047-1070.
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Zhuo-Heng He, Meng Wang & Xin Liu. (2020) On the general solutions to some systems of quaternion matrix equations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114:2.
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Abdur Rehman, Ivan Kyrchei, Muhammad Akram, Ilyas Ali & Abdul Shakoor. (2019) Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations. Abstract and Applied Analysis 2019, pages 1-18.
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Abdur Rehman, Ivan Kyrchei, Ilyas Ali, Muhammad Akram & Abdul Shakoor. (2019) The General Solution of Quaternion Matrix Equation Having -Skew-Hermicity and Its Cramer’s Rule . Mathematical Problems in Engineering 2019, pages 1-25.
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Ivan Kyrchei. (2019) Cramer’s Rules of $$\pmb {\eta }$$-(Skew-)Hermitian Solutions to the Quaternion Sylvester-Type Matrix Equations. Advances in Applied Clifford Algebras 29:3.
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Zhuo-Heng He. (2019) A System of Coupled Quaternion Matrix Equations with Seven Unknowns and Its Applications. Advances in Applied Clifford Algebras 29:3.
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Si-Tao Ling, Zhi-Gang Jia, Xin Lu & Bing Yang. (2019) Matrix LSQR algorithm for structured solutions to quaternionic least squares problem. Computers & Mathematics with Applications 77:3, pages 830-845.
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Zhuo-Heng He. (2018) Structure, Properties and Applications of Some Simultaneous Decompositions for Quaternion Matrices Involving $$\phi $$ ϕ -Skew-Hermicity. Advances in Applied Clifford Algebras 29:1.
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Ivan I. Kyrchei. (2019) Cramer’s rules for the system of quaternion matrix equations with η -Hermicity . 4open 2, pages 24.
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Ivan I. Kyrchei. (2018) Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations. Journal of Mathematics 2018, pages 1-12.
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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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Xiangrong Nie, Qingwen Wang & Yang Zhang. (2017) A System of Matrix Equations over the Quaternion Algebra with Applications. Algebra Colloquium 24:02, pages 233-253.
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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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Xiaotao Sun. (2017) Factorization of Generalized Theta Functions Revisited. Algebra Colloquium 24:01, pages 1-52.
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G. Ebadi & S. Rashedi. (2016) The General Solution to a System of Eight Quaternion Matrix Equations with Applications. Iranian Journal of Science and Technology, Transactions A: Science 40:2, pages 91-102.
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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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Xiang Zhang. (2016) A system of generalized Sylvester quaternion matrix equations and its applications. Applied Mathematics and Computation 273, pages 74-81.
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Abdur Rehman & Qing-Wen Wang. (2015) A system of matrix equations with five variables. Applied Mathematics and Computation 271, pages 805-819.
Crossref
Abdur Rehman, Qing-Wen Wang & Zhuo-Heng He. (2015) Solution to a system of real quaternion matrix equations encompassing η-Hermicity. Applied Mathematics and Computation 265, pages 945-957.
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