Results 31 to 40 of about 606 (79)
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
On linear combinations of two idempotent matrices over an arbitrary field [PDF]
, 2010 Given an arbitrary field K and non-zero scalars a and b, we give necessary and sufficient conditions for a matrix A in M_n(K) to be a linear combination of two idempotents with coefficients a and b. This extends results previously obtained by Hartwig and
Clément de Seguins Pazzis +3 more
core +2 more sources
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
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
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
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
The Resolvent Average for Positive Semidefinite Matrices [PDF]
, 2009 We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it ...
Bauschke, Heinz H. +2 more
core +3 more sources
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
Unitarily invariant norm inequalities for operators
Journal of the Egyptian Mathematical Society, 2012 We present several norm inequalities for Hilbert space operators. In particular, we prove that if A1,A2,…,An∈B(H), then |||A1A2∗+A2A3∗+⋯+AnA1∗|||⩽∑i=1nAiAi∗for all unitarily invariant norms. We also show that if A1,A2,A3,A4 are projections in B(H), then ∑
M. Erfanian Omidvar +2 more
doaj +1 more source