Results 21 to 30 of about 96 (95)

Invariance of recurrence sequences under a galois group

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 327-334, 1996., 1995
Let F be a Galois field of order q, k a fixed positive integer and R = Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F‐vector space Γk(F)( = Γ(L)) of all sequences over Fk×1 is a left R‐module. For any regular f(D) ∈ R, Ωk(f(D)) = {S ∈ Γk(F) : f(D)S
Hassan Al-Zaid, Surjeet Singh
wiley   +1 more source

Non-commutative standard polynomials applied to matrices

, 2016
International audienceThe Amitsur–Levitski Theorem tells us that the standard polynomial in 2n non-commuting indeterminates vanishes identically over the matrix algebra M n (K). For K = R or C and 2 ≤ r ≤ 2n − 1, we investigate how big S r (A 1 ,. .. , A
Serre, Denis
core   +1 more source

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
wiley   +1 more source

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
doaj   +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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

Infants of mothers with early remitted clinical depression and mothers with no postpartum depression: Adaptive functioning in the second year of life

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, Nanmathi Manian, Lauren M. Henry   +2 more
wiley   +1 more source

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
wiley   +1 more source

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
doaj   +1 more source