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Linear and Multilinear Algebra Volume 38, 1995 - Issue 3
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Original Articles

The matrix equation AXB+CYD=Eover a simple artinian ring

Huang Liping Department of Basic Sciences, Xiangtan Mining Institute, Xiangtan, 411201, P.R. China
&
Zeng Qingguang Department of Basic Sciences, Xiangtan Mining Institute, Xiangtan, 411201, P.R. China
Pages 225-232 | Published online: 30 May 2007

Citations (24)

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Read on this site (6)

Zhuo-Heng He & Qing-Wen Wang. (2014) The η-bihermitian solution to a system of real quaternion matrix equations. Linear and Multilinear Algebra 62:11, pages 1509-1528.
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Qing-Wen Wang & Zhuo-Heng He. (2012) Some matrix equations with applications†. Linear and Multilinear Algebra 60:11-12, pages 1327-1353.
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Shifang Yuan & Anping Liao. (2011) Least squares solution of the quaternion matrix equation with the least norm. Linear and Multilinear Algebra 59:9, pages 985-998.
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Minghui Wang, Musheng Wei & Yan Feng. (2010) An iterative algorithm for a least squares solution of a matrix equation. International Journal of Computer Mathematics 87:6, pages 1289-1298.
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Huang Liping. (1998) The minimal polynomial of a matrix . Linear and Multilinear Algebra 45:2-3, pages 99-107.
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Huang Liping. (1996) The solvability of linear matrix equations over a central simple algebra. Linear and Multilinear Algebra 40:4, pages 353-363.
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Articles from other publishers (18)

Abdur Rehman, Israr Ali Khan, Rukhshanda Anjum & Iftikhar Hussain. (2021) Solvability Conditions and General Solution of a System of Matrix Equations Involving η-Skew-Hermitian Quaternion Matrices. Symmetry 13:10, pages 1825.
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Huiting Zhang, Hairui Zhang, Lina Liu & Yongxin Yuan. (2020) A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $. AIMS Mathematics 6:3, pages 2579-2589.
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Wei-Ru Xu, Guo-Liang Chen & Xing-Ping Sheng. (2018) Analytical best approximate Hermitian and generalized skew-Hamiltonian solution of matrix equation . Computers & Mathematics with Applications 75:10, pages 3702-3718.
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Sheng Chen & Yunbo Tian. (2016) On T-Sylvester equations over commutative rings. Journal of the Franklin Institute 353:5, pages 1102-1108.
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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.
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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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Yi-Fen Ke & Chang-Feng Ma. (2015) Alternating direction method for generalized Sylvester matrix equation AXB + CYD = E. Applied Mathematics and Computation 260, pages 106-125.
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Masoud Hajarian. (2014) Efficient Iterative Solutions to General Coupled Matrix Equations. International Journal of Automation and Computing 10:5, pages 481-486.
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Ning Li, Jing Jiang & Guang-Jing Song. (2012) Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation. Journal of Applied Mathematics and Computing 42:1-2, pages 19-40.
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Mehdi Dehghan & Masoud Hajarian. (2010) The Reflexive and Anti-Reflexive Solutions of a Linear Matrix Equation and Systems of Matrix Equations. Rocky Mountain Journal of Mathematics 40:3.
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Xingping Sheng & Guoliang Chen. (2010) An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation . Journal of Computational and Applied Mathematics 233:11, pages 3030-3040.
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Qing-Wen Wang, Hai-Xia Chang & Chun-Yan Lin. (2008) P-(skew)symmetric common solutions to a pair of quaternion matrix equations. Applied Mathematics and Computation 195:2, pages 721-732.
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An-Ping Liao, Zhong-Zhi Bai & Yuan Lei. (2005) Best Approximate Solution of Matrix Equation AXB+CYD=E. SIAM Journal on Matrix Analysis and Applications 27:3, pages 675-688.
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Qing-Wen Wang. (2004) A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity. Linear Algebra and its Applications 384, pages 43-54.
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Liping Huang. (2002) To solve matrix equation ΣA i XB i =C by the Smith normal form. Applied Mathematics-A Journal of Chinese Universities 17:1, pages 109-118.
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Liping Huang. (2000) On two questions about quaternion matrices. Linear Algebra and its Applications 318:1-3, pages 79-86.
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Huang Liping. (1998) The quaternion matrix equation ΣA i XB i =E. Acta Mathematica Sinica 14:1, pages 91-98.
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Liping Huang & Jianzhou Liu. (1997) The extension of Roth's theorem for matrix equations over a ring. Linear Algebra and its Applications 259, pages 229-235.
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