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1.
强P除环上方阵的酉相似理论(Ⅱ)   总被引:11,自引:3,他引:8  
This is a continuation of the previous paper ( 1 ) . In this paper , a useful basic theorem that every selfconjugate matrix over the strong p division ring Ω is unitary similar to a tridiagorial matrix over the conter of Ω is given thus all of famous results involving selfconjugate matrices, positivedefinite selfcon jugate matrices, nonnegative selfconjugate matrix in the ordiniry com plex matrix theory are generalized to selfconjugate matrices over Ω . and Sigular decomuposition as well as polar decomposition in the ordinary complex matrix theory are also generalized to matrices over Ω .  相似文献   

2.
The matrix equation AXB = E with the constraint PX=sXP is considered,where P is a given Hermitian matrix satisfying p~2=I and s=±1.By an eigenvalue decomposition of P,the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P.A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented.Moreover,a similar problem of the matrix equation with generalized constraint is discussed.  相似文献   

3.
In this paper,the Hermitian reflexive(Anti-Hermitian reflexive)least-squares so-lutions of matrix equations(AX = B,XC = D)are considered.With special properties of partitioned matrices and Hermitian reflexive(Anti-Hermitian reflexive)matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.  相似文献   

4.
This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator:-△pu=λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.  相似文献   

5.
In this article, the generalized reflexive solution of matrix equations (AX = B, XC = D) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.  相似文献   

6.
强p除环上方阵的酉相似理论(Ⅲ)   总被引:4,自引:2,他引:2  
In this third paper, the famous Schur theorem that an n× n complex matrix is unitary similar to an upper triangular matrix is generalized to the socalled ∑-lizable matrix over the strong p-division ring Ω, where ∑ is the algebraically closed extension field of the center of Ω , and ∑?Ω.The generalized Schur's identity and other results involving the general-ized normal matrix over Ω is obtained by using this generalized Schur theorem.  相似文献   

7.
Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k(X) of function algebra on a finite set X are considered.  相似文献   

8.
In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method.  相似文献   

9.
We study perturbation bound and structured condition number about the minimal nonnegative solution of nonsymmetric algebraic Riccati equation, obtaining a sharp perturbation bound and an accurate condition number. By using the matrix sign function method we present a new method for finding the minimal nonnegative solution of this algebraic Riccati equation. Based on this new method, we show how to compute the desired M-matrix solution of the quadratic matrix equation X^2 - EX - F = 0 by connecting it with the nonsymmetric algebraic Riccati equation, where E is a diagonal matrix and F is an M-matrix.  相似文献   

10.
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^*X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.  相似文献   

11.
有限维中心代数上矩阵方程组的广对称解与斜广对称解   总被引:1,自引:0,他引:1  
设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.  相似文献   

12.
设Ω是一个特征非2的具有对合反自同构的有限维中心代数.本文研究Ω上的两个矩阵方程组,分别给出了其有一般解和次(斜)自共轭解的充要条件.  相似文献   

13.
§1. IntroductionandPreliminariesTheconsiderableprogresseshavebeenmadeinthetheoryofmatricesoverskewfieldssinceprofessorXieBandjiesimportantpaper[1]waspublished.Itiswellknownthatmatrixequationisoneofimportantcontentsofmatrixstudy.In[2-4],fivetypesofma…  相似文献   

14.
李样明 《数学杂志》2002,22(3):281-286
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   

15.
Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of Ln(Ω)Ln(Ω)-1 and Φn(z;Ω)Φn(z;Ω)-1 where Ω(z) = Ω(z) + zδ(z - w); |w| > 1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, Ln ( @ ) means the leading coefficient of the orthonormal matrix polynomials Φn(z; @ ).Finally, we deduce the asymptotic behavior of Φn (w;Ω)Φn (w;Ω) * in the case when M=I.  相似文献   

16.
许永华 《数学学报》1979,22(3):303-315
<正> 为了进一步对本原环结构的研究,本文引进规范环的概念,我们说环R是规范的,若R是一个线性变换完全环并且及的基座对于任一对应基{E_i}皆有=∑RE_i=∑E_iR.容易知道,满足单侧理想极小条件的单纯环必是规范的.  相似文献   

17.
In this paper, the necessary and sufficient conditions for the solvability of matrix equation AHXB=C over the reflexive or anti-reflexive matrices are given, and the general expression of the solution for a solvable case is obtained. Moreover, the relative optimal approximation problem is considered. The explicit expressions of the optimal approximation solution and the minimum norm solution are both provided.  相似文献   

18.
TheMetapositiveDefiniteSelf-ConjugateSolutionoftheMatrixEquationAXB=Cover a Skew FieldWangQingwen(王卿文)(DepartmentofMath.,Chan...  相似文献   

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