共查询到20条相似文献,搜索用时 125 毫秒
1.
主要针对交换环上两类矩阵的保持问题进行展开:(1)刻画了交换环上全矩阵空间和上三角形矩阵空间的保持反对合矩阵映射的形式.(2)研究了交换环上n阶上三角形矩阵空间的保持伴随矩阵映射的形式. 相似文献
2.
利用fusion环的一些性质,基于给定的未定型广义Cartan矩阵,构造了两类fusion环.结果表明这两类fusion环均为类群fusion环. 相似文献
3.
该文讨论了两类线性流形上矩阵方程B^TXB=D的反对称解和反对称最佳逼近解存在的条件,给出了通解的一般表达式,同时解决了解对给定矩阵的唯一最佳逼近问题. 相似文献
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设F和Ω分别表示一个对合反自同构的体,一个加强P除环,本文定义了Ω上的亚(半)正定矩阵,给出了矩阵方程AXA^*=B在F上有(斜)自共轭矩阵解及在Ω上有亚(半)正定矩阵解的充要条件及其解集的显式表示。 相似文献
6.
先建立除环上的矩阵范畴,并证明这个范畴是Abel范畴,然后利用范畴论中的结论给出除环上矩阵方程AXB=D有解的条件。 相似文献
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设HF为域F上的广义四元数除环,ChF≠2。本文利用拟线性变换T(X)=AX-DXB讨论HF上矩阵方程AX-DXB=R的求解问题,获得了上方程存在(唯一)解的几个充分必要条件,并给出了解的显式公式。 相似文献
9.
设Fq是含有q个元素的有限域,其中q=pr,r≥1,p是奇素数.研究了有限域Fq上Markoff-Hurwitz类型方程,并给出了当其增广次数矩阵在剩余类环Z/(q-1)Z中可逆时其解数公式的组合证明方法.进一步研究了其推广形式,并得到了此推广形式的方程在特殊条件下的解数公式. 相似文献
10.
矩阵方程A^TXB=C的正定和半正定解 总被引:5,自引:1,他引:4
何楚宁 《高校应用数学学报(A辑)》1997,(4):475-480
给出了矩阵方程A^TXB=C在正定和半正定矩阵类中有解的充要条件及解的一般表达式。 相似文献
11.
A method of explicit factorization of matrix functions of second order is proposed. The method consists of reduction of this problem to two scalar barrier problems and a finite system of linear equations. Applications to various classes of singular integral equations and equations with Toeplitz and Hankel matrices are given. 相似文献
12.
Aleksandar S. Cvetkovi? 《Linear algebra and its applications》2008,429(10):2401-2414
In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others. 相似文献
13.
B. Z. Shavarovskii 《Computational Mathematics and Mathematical Physics》2007,47(12):1902-1911
Two classes of matrix polynomial equations with commuting coefficients are examined. It is shown that the equations in one class have complete sets of solutions, whereas the equations in the other class are unsolvable. A method is given for finding the solution set of an equation in the former class. 相似文献
14.
D. G. Korenevskii 《Ukrainian Mathematical Journal》2000,52(2):260-266
We establish the relationship (equivalence) between the spectral and algebraic (coefficient) criteria (the latter is represented in terms of the Sylvester matrix algebraic equation) of mean-square asymptotic stability for three classes of systems of linear equations with varying random perturbations of coefficients, namely, the ltô differential stochastic equations, difference stochastic equations with discrete time, and difference stochastic equations with continuous time. 相似文献
15.
The stability of various factorizations of self-adjoint rational matrix functions and matrix polynomials, as well as of hermitian solutions of symmetric matrix algebraic Riccati equations, is studied. In the first part of this paper results on stability of certain classes of invariant subspaces of a matrix which is self-adjoint in an indefinite inner product were obtained. These results serve as the main tools in the investigation. 相似文献
16.
A. G. Mazko 《Ukrainian Mathematical Journal》1998,50(7):1058-1066
We propose algebraic methods for the investigation of the spectrum and structure of solutions of degenerate dynamical systems.
These methods are based on the construction and solution of new classes of matrix equations. We prove theorems on the inertia
of solutions of the matrix equations, which generalize the well-known properties of the Lyapunov equation.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 930–936, July, 1998. 相似文献
17.
《复变函数与椭圆型方程》2012,57(6):485-494
We consider two classes of systems of partial differential equations of first order. One consists of generalized Stokes-Beltrami equations $ Aw_z = w^*_z $ , $ \lambda Bw_{\bar z} -w^*_{\bar z} $ with square matrices A and B and a scalar factor u . The other may be written in matrix notation as $ v_{\bar z} = c{\bar v} $ where c denotes a square matrix. This system is known as a Pascali system. Both systems are in close connections to certain systems of second order for which the solutions can be represented using particular differential operators. On the basis of these relations we give the solutions of the first order systems explicitly. 相似文献
18.
The notion of a distributed-order Hilfer–Prabhakar derivative is introduced, which reduces in special cases to the existing notions of fractional or distributed-order derivatives. The stability of two classes of distributed-order Hilfer–Prabhakar differential equations, which are generalizations of all distributed or fractional differential equations considered previously, is analyzed. Sufficient conditions for the asymptotic stability of these systems are obtained by using properties of generalized Mittag-Leffler functions, the final-value theorem, and the Laplace transform. Stability conditions for such systems are introduced by using a new definition of the inertia of a matrix with respect to the distributed-order Hilfer–Prabhakar derivative. 相似文献
19.
A. N. Mironov 《Mathematical Notes》2013,94(3-4):369-378
On the basis of determining equations written out in terms of Laplace invariants, some classes of Bianchi equations of third order similar to well-known classes of hyperbolic equations with two independent variables are singled out. 相似文献
20.
A. N. Mironov 《Differential Equations》2013,49(12):1524-1533
On the basis of defining equations written out in terms of Laplace invariants, we single out some classes of fourth-order Bianchi equations similar to the well-known classes of hyperbolic equations with two independent variables admitting Lie algebras of maximum dimension. 相似文献