Results 21 to 30 of about 65 (65)
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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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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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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Infant Mental Health Journal: Infancy and Early Childhood, Volume 45, Issue 4, Page 397-410, July 2024.Abstract Whether and how remitted clinical depression in postpartum motherhood contributes to poor infant adaptive functioning is inconclusive. The present longitudinal study examines adaptive functioning in infants of mothers diagnosed as clinically depressed at 5 months but remitted at 15 and 24 months. Fifty‐five U. S.
Marc H. Bornstein +2 more
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A note of equivalence classes of matrices over a finite field
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 2, Page 279-287, 1981., 1981 Let Fqm×m denote the algebra of m × m matrices over the finite field Fq of q elements, and let Ω denote a group of permutations of Fq. It is well known that each ϕϵΩ can be represented uniquely by a polynomial ϕ(x)ϵFq[x] of degree less than q; thus, the group Ω naturally determines a relation ∼ on Fqm×m as follows: if A,BϵFqm×m then A ~ B if ϕ(A) = B ...
J. V. Brawley, Gary L. Mullen
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On relationships between two linear subspaces and two orthogonal projectors
Special Matrices, 2019 Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
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