Results 291 to 300 of about 247,997 (332)
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Lyapunov's matrix equation with system matrix in companion form
International Journal of Control, 1993Abstract A simple method for solving Lyapunov's matrix equation for linear continuous systems with the system matrix in companion form is proposed. The method involves the inversion of the Hurwitz matrix. A necessary and sufficient condition for the existence of a solution to the equation is also obtained.
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Iterative methods for solving linear matrix equation and linear matrix system
International Journal of Computer Mathematics, 2010In this paper, an efficient iterative method is presented to solve the linear matrix equation [image omitted] (X) = E with real matrix X. By this iterative method, the solvability of the linear matrix equation can be determined automatically. When the matrix equation is consistent, then, for any initial matrix X0, a solution can be obtained within ...
Youfeng Su, Guoliang Chen 0002
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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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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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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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International Journal of Computational Mathematics
Sylvester matrix equations play important roles in control and system theory. We consider a class of the generalized coupled Sylvester quaternion matrix equations, which includes a lot of special matrix equations such as Stein matrix equation, Lyapunov ...
Yifen Ke +3 more
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Sylvester matrix equations play important roles in control and system theory. We consider a class of the generalized coupled Sylvester quaternion matrix equations, which includes a lot of special matrix equations such as Stein matrix equation, Lyapunov ...
Yifen Ke +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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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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Constraint Solution of a Classical System of Quaternion Matrix Equations and Its Cramer’s Rule
Iranian Journal of Science and Technology, Transactions A: Science, 2021A. Rehman +4 more
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