Results 251 to 260 of about 175,846,736 (289)

A system of matrix equations and its applications

Science China Mathematics, 2013
For the following system of matrix equations, \(A_1X = {C_1}\), \({A_2}Y = {C_2}\), \(Y{B_2} = {D_2}\), \(Y = {Y^ * }\), \({A_3}Z = {C_3}\), \(Z{B_3} = {D_3}\), \(Z = {Z^ * }\), \({B_4}X + {({B_4}X)^ * } + {C_4}YC_4^ * + {D_4}ZD_4^ * = {A_4}\), solvability conditions are proved, a general solution is formulated, and the maximal and minimal ranks and ...
Wang, QingWen, He, ZhuoHeng
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Lyapunov's matrix equation with system matrix in companion form

International Journal of Control, 1993
Abstract 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, 2010
In 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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Solving Matrix Diophantine Equations by Inverting a Square Nonsingular System of Equations

IEEE Transactions on Circuits and Systems II: Express Briefs, 2004
A method for solving the Diophantine equation using a nonsingular matrix equation system is proposed in this note. A scheme of setting up a system with the same number of variables as equations is described. An analytical approach to ensure the invertibility of the system formed is given. Examples presented show the simplicity of the method.
K. S. Yeung, Tse-Min Chen
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$$\eta $$-Hermitian Solution to a System of Quaternion Matrix Equations

Bulletin of the Malaysian Mathematical Sciences Society, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xin, He, Zhuo-Heng
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Solvability of systems of linear matrix equations subject to a matrix inequality

Linear and Multilinear Algebra, 2016
In 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, 2017
We 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, Wang, Qingwen, Zhang, Yang   +2 more
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A constrained system of matrix equations

Computational and Applied Mathematics, 2022
Yang-Fan Xu, Qing-Wen Wang 0001, Long-Sheng Liu, Mahmoud Saad Mehany   +3 more
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Matrix Functions and Systems of Differential Equations

2015
In 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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On iterative solutions of a class of matrix equations in systems and control

Proceedings of the 2004 American Control Conference, 2004
In 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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