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Communications in Algebra Volume 29, 2001 - Issue 6
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Original Articles

JORDAN CANONICAL FORM OF A PARTITIONED COMPLEX MATRIX AND ITS APPLICATION TO REAL QUATERNION MATRICES

Fuzhen Zhang Department of Math Science and Technology, Nova Southeastern University, Fort Lauderdale, Florida, 33314, U.S.A.
&
Y. Wei Department of Math Science and Technology, Nova Southeastern University, Fort Lauderdale, Florida, 33314, U.S.A.
Pages 2363-2375 | Received 01 Nov 1999, Published online: 16 Aug 2006

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Qing-Wen Wang, Shao-Wen Yu & Qin Zhang. (2009) The Real Solutions to a System of Quaternion Matrix Equations with Applications. Communications in Algebra 37:6, pages 2060-2079.
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Chen Ling, Liqun Qi & Hong Yan. Minimax Principle for Eigenvalues of Dual Quaternion Hermitian Matrices and Generalized Inverses of Dual Quaternion Matrices. Numerical Functional Analysis and Optimization 0:0, pages 1-26.
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Articles from other publishers (21)

Haojin Li & Sitian Qin. (2024) A Hessian-based zeroing neurodynamic approach for quaternion-variable time-varying constrained optimization problems. Neurocomputing 564, pages 126937.
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Zhigang Jia, Qianyu Wang, Hong-Kui Pang & Meixiang Zhao. (2023) Computing Partial Quaternion Eigenpairs with Quaternion Shift. Journal of Scientific Computing 97:2.
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Dan Chen, Michal Fečkan & JinRong Wang. (2022) Linear quaternion-valued difference equations: Representation of solutions, controllability, and observability. Journal of Mathematical Physics 63:11.
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Dan Chen, Michal Fečkan & JinRong Wang. (2021) On the Stability of Linear Quaternion-Valued Differential Equations. Qualitative Theory of Dynamical Systems 21:1.
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Chao Wang, Zhien Li & Ravi P. Agarwal. (2022) A New Quaternion Hyper-Complex Space with Hyper Argument and Basic Functions via Quaternion Dynamic Equations. The Journal of Geometric Analysis 32:2.
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Zicong Xia, Yang Liu, Jianquan Lu, Jinde Cao & Leszek Rutkowski. (2021) Penalty Method for Constrained Distributed Quaternion-Variable Optimization. IEEE Transactions on Cybernetics 51:11, pages 5631-5636.
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Song Huang & Fuli He. (2021) On the Second Lyapunov Method for Quaternionic Differential Equations. Qualitative Theory of Dynamical Systems 20:2.
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Leping Suo, Michal Fečkan & JinRong Wang. (2021) Quaternion-Valued Linear Impulsive Differential Equations. Qualitative Theory of Dynamical Systems 20:2.
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Zhien Li, Chao Wang, Ravi P. Agarwal & Donal O'Regan. (2020) Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales. Studies in Applied Mathematics 146:1, pages 139-210.
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Dong Cheng, Kit Ian Kou & Yong Hui Xia. (2020) Floquet Theory for Quaternion-Valued Differential Equations. Qualitative Theory of Dynamical Systems 19:1.
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Yang Liu, Yanling Zheng, Jianquan Lu, Jinde Cao & Leszek Rutkowski. (2020) Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach. IEEE Transactions on Neural Networks and Learning Systems 31:3, pages 1022-1035.
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Kit Ian Kou, Wan-Kai Liu & Yong-Hui Xia. (2019) Solve the linear quaternion-valued differential equations having multiple eigenvalues. Journal of Mathematical Physics 60:2.
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Yanling Zheng, Yang Liu & Jinde Cao. (2018) One-Layer Neural Network for Nonlinear Convex Programming with Linear Constraints. One-Layer Neural Network for Nonlinear Convex Programming with Linear Constraints.
Zhen Feng Cai & Kit Ian Kou. (2017) Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients. Qualitative Theory of Dynamical Systems 17:2, pages 441-462.
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Zhigang Jia, Musheng Wei & Sitao Ling. (2013) A new structure-preserving method for quaternion Hermitian eigenvalue problems. Journal of Computational and Applied Mathematics 239, pages 12-24.
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Terry A. Loring. (2012) Factorization of matrices of quaternions. Expositiones Mathematicae 30:3, pages 250-267.
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Sen Yu, Wei Cheng & Lianggui feng. 2010. Information Computing and Applications. Information Computing and Applications 70 77 .
Fuzhen Zhang. (2007) Geršgorin type theorems for quaternionic matrices. Linear Algebra and its Applications 424:1, pages 139-153.
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Leiba Rodman. 2007. System Theory, the Schur Algorithm and Multidimensional Analysis. System Theory, the Schur Algorithm and Multidimensional Analysis 199 254 .
D. Alpay, A.C.M. Ran & L. Rodman. (2006) Basic classes of matrices with respect to quaternionic indefinite inner product spaces. Linear Algebra and its Applications 416:2-3, pages 242-269.
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G. Opfer. (2005) The conjugate gradient algorithm applied to quaternion valued matrices. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 85:9, pages 660-672.
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