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Matrix Functions and Systems of Differential Equations
2015In this chapter we give an introduction to the area of matrix functions. We first define general matrix functions and derive their most important properties. Using the examples of network analysis and chemical reactions, we illustrate how matrix functions arise naturally in applications. The network analysis example involves the exponential function of
Jörg Liesen, Volker Mehrmann
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Solvability of systems of linear matrix equations subject to a matrix inequality
Linear and Multilinear Algebra, 2016In this paper, the solvability conditions and the explicit expressions of the Hermitian solutions to the system of matrix equationsand the Hermitian nonnegative definite solutions to the system of matrix equationsare, respectively, put forward, by making full use of the generalized inverse and the rank of matrices.
Juan Yu, Shu-qian Shen
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A System of Matrix Equations over the Quaternion Algebra with Applications
Algebra Colloquium, 2017We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations [Formula: see text] and [Formula: see text] over the quaternion algebra ℍ, and present an expression of the general solution to this system when it is solvable.
Nie, Xiangrong +2 more
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A constrained system of matrix equations
Computational and Applied Mathematics, 2022Yang-Fan Xu +3 more
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On iterative solutions of a class of matrix equations in systems and control
Proceedings of the 2004 American Control Conference, 2004In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss-Seidel iterations as its special cases. We give the necessary and sufficient conditions for convergence of the iterative solutions.
Feng Ding 0001, Tongwen Chen
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$$\eta $$-Hermitian Solution to a System of Quaternion Matrix Equations
Bulletin of the Malaysian Mathematical Sciences Society, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xin, He, Zhuo-Heng
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The complexity of matrix rank and feasible systems of linear equations
Computational Complexity, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eric Allender +2 more
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On Solvability of Hermitian Solutions to a System of Five Matrix Equations
Mediterranean Journal of Mathematics, 2013The main results of this paper are the following: (1) Necessary and sufficient conditions for the existence of Hermitian solutions \({X_1}\) and \({X_2}\) of the matrix equations \({A_1}{X_1} = {C_1}\), \({X_1}{B_1} = {C_2}\), \({A_2}{X_2} = {C_3}\), \({X_2}{B_2} = {C_4}\), \({A_3}{X_1}A_3^ * + {A_4}{X_2}A_4^ * = {C_5}\) are given.
Yu, Shao-Wen, Song, Guang-Jing
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On the solution of the covariance matrix differential equation for singular systems
International Journal of Computer Mathematics, 1998State space formulation for singular linear stationary random inputs are presented. A covariance matrix differential equation is derived and a new technique for solving this equation using Kronecker product is included. An example is provided to illustrate the applicability of the proposed method.
Masoud Shafiee, Mohsen Razzaghi
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A Constraint System of Generalized Sylvester Quaternion Matrix Equations
Advances in Applied Clifford Algebras, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdur Rehman +4 more
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