Results 21 to 30 of about 560 (104)
The Matrix Equation XA − AX = Xαg(X) over Fields or Rings
Algebra, Volume 2014, Issue 1, 2014., 2014 Let n,α∈N≥2 and let K be an algebraically closed field with characteristic 0 or greater than n. We show that if f ∈ K[X] and A, B ∈ Mn(K) satisfy [A, B] = f(A), then A, B are simultaneously triangularizable. Let R be a reduced ring such that n! is not a zero divisor and let A be a generic matrix over R; we show that X = 0 is the sole solution of AX ...
Gerald Bourgeois, Zhongshan Li
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Hypersymmetric functions and Pochhammers of 2 × 2 nonautonomous matrices
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 59, Page 3151-3170, 2004., 2004 We introduce the hypersymmetric functions of 2 × 2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials) of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2 × 2 matrices, having a high degree
A. F. Antippa
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Maximizing the determinant for a special class of block‐partitioned matrices
Mathematical Problems in Engineering, Volume 2004, Issue 1, Page 49-61, 2004., 2004 An analytical solution is found for the maximum determinant of a block‐partitioned class of matrices with constant trace for each block. As an immediate application of this result, the maximum determinant of a sum of Kronecker products is derived.
Otilia Popescu +2 more
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The core inverse and constrained matrix approximation problem
Open Mathematics, 2020 In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:||Mx−b||F=minsubjecttox∈ℛ(M),||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in ...
Wang Hongxing, Zhang Xiaoyan
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Direct methods for matrix Sylvester and Lyapunov equations
Journal of Applied Mathematics, Volume 2003, Issue 6, Page 277-303, 2003., 2003 We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels‐Stewart method for A1X + XA2 + D = 0 and Hammarling′s method for AX + XAT + BBT = 0 with A stable. We construct three schemes for solving the unitarily reduced quasitriangular systems. We also construct a new rank‐1 updating scheme in Hammarling′s method.
Danny C. Sorensen, Yunkai Zhou
wiley +1 more source
The Cayley transform of Banach algebras
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 7, Page 427-428, 2002., 2002 The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn = 0) if and only if it is the Cayley transform CA = (I−A)−1(I + A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.
Zhidong Pan
wiley +1 more source
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
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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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Conservation laws for multidimensional systems and related linear algebra problems [PDF]
, 2002 We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives.
Bocharov A V +11 more
core +8 more sources