Results 41 to 50 of about 644 (117)
Generalized Pell Equations for 2 × 2 Matrices
Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
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Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0) [PDF]
, 2012 In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 01, a new sufficient condition for the existence of a unique positive definite solution for the ...
Li, Jing
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Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 91-102, 1994., 1994 In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. Solving appropriate algebraic matrix equations a closed form expression for the matrix coefficient of the series are ...
E. Navarro, L. Jódar, R. Company
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Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables [PDF]
, 2015 Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schr\"odinger equations depending on two variables and of nonlinear wave equations depending on three ...
Fritzsche, Bernd +3 more
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On the sum of powers of square matrices
Operators and Matrices, 2019 Given a 2×2 matrix A , we obtain the formula for sum of An , (n∈ Z) , using its trace and determinant only; this includes the negative powers in the case of a nonsingular matrix too. Here we mean by sum, the sum of all the entries of the matrix.
D. J. Karia, K. Patil, H. Singh
semanticscholar +1 more source
Generalized Green′s functions for higher order boundary value matrix differential systems
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 3, Page 523-535, 1992., 1992 In this paper, a Green′s matrix function for higher order two point boundary value differential matrix problems is constructed. By using the concept of rectangular co‐solution of certain algebraic matrix equation associated to the problem, an existence condition as well as an explicit closed form expression for the solution of possibly not well‐posed ...
R. J. Villanueva, L. Jodar
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On the Yang-Baxter-like matrix equation for rank-two matrices
Open Mathematics, 2017 Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX.
Zhou Duanmei, Chen Guoliang, Ding Jiu
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A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.Matrix equations are of foundational importance in the modeling, investigation, and control of dynamical systems. This review discusses various classes of matrix equations, their solutions, and their relevance in control theory and dynamical systems.
Chacha Stephen Chacha, Arpan Hazra
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Stable matrices, the Cayley transform, and convergent matrices
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 77-81, 1991., 1991 The main result is that a square matrix D is convergent () if and only if it is the Cayley transform CA = (I − A) −1(I + A) of a stable matrix A, where a stable matrix is one whose characteristic values all have negative real parts. In passing, the concept of Cayley transform is generalized, and the generalized version is shown closely related to the ...
Tyler Haynes
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A preconditioned AOR iterative scheme for systems of linear equations with L-matrics
Open Mathematics, 2019 In this paper we investigate theoretically and numerically the new preconditioned method to accelerate over-relaxation (AOR) and succesive over-relaxation (SOR) schemes, which are used to the large sparse linear systems.
Wang Hongjuan
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