Results 41 to 50 of about 635 (110)
Inequalities for ranks of matrix expressions involving generalized inverses
Journal of Inequalities and Applications, 2014 In this paper, we present several inequalities for ranks of the matrix expressions D−ABXAB with respect to the choice of X, where X is taken, respectively, as B(1)A(1), B(1,2)A(1,2), B(1,3)A(1,3), B(1,4)A(1,4), B(1,2,3)A(1,2,3) as well as B(1,2,4)A(1,2,4)
Zhiping Xiong
semanticscholar +2 more sources
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. P. 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
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
On the matrix equation $XA+AX^T =0$, II: Type 0-I interactions
, 2013 The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved.
Chan, Alice Zhuo-Yu +3 more
core +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
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
doaj +1 more source
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
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