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1.
二阶线性矩阵微分系统的振动性   总被引:4,自引:0,他引:4  
本文研究了矩阵微分系统(P(t)Y′)′+Q(t)Y=0,t∈[t0,∞).其中P,Q和Y是n×n实连续矩阵函数,且P(t)和Q(t)是对称的.P(t)是正定矩阵(P(t)>0,t∈[t0,∞)).利用推广的Riccati变换,得到了系统(1)振动的若干新判据.所得结果改进了Erbe,Kong和Ruan的相应结果.  相似文献   

2.
文[1]定义了广义正定矩阵集合P(I).文[2]定义了较P(I)更广泛的另一个广义正定矩阵集合P(S+).本文把P(I)中矩阵的某些性质,推广到P(S+)中从而丰富了P(S+)矩阵集合的结果。  相似文献   

3.
非对称半正定矩阵的一些性质阳本傅(成都师范高等专科学校数学系611930)设A是n阶实矩阵(不一定对称),如果对任意实n元向量X,均有X′AX0(>0),就称A为半正定矩阵(正定矩阵).本文给出半正定矩阵的一种合同标准形,由此比较简捷地得出了半正定...  相似文献   

4.
一个n×n实四元数矩阵称为实部半正定(或正定)矩阵,如果对于任意的非零n维四元数列向量x,有Re[xAx]≥0(或>0).本文给出了四元数矩阵方程AX=B有实部半正定(或正定)矩阵解的充要条件及其通解的表达式,并给出了四元数分块阵为实部半正定(或正定)矩阵的一个判别法则  相似文献   

5.
M—矩阵的等价表征   总被引:15,自引:0,他引:15  
本文引进了按环路弱不约非零元素对角占优的概念,讨论了M-矩阵的等价条件,给出了M-矩阵的两个等价表征,改进与推广了(1),(2),(5),(9)的相应结果。  相似文献   

6.
正交矩阵的两个特征性质   总被引:1,自引:0,他引:1  
正交矩阵的两个特征性质李先崇(贵州师范大学数学系550001)本文中的矩阵均为实矩阵.A=(aij})为方阵,Aij表示aij的代数余子式,A′,A*分别表示A的转置和伴随矩阵,n阶矩阵A=(aij)的迹Tr(A)=∑ni=1ai.En表示n阶单位矩...  相似文献   

7.
求矩阵秩的一种新算法张裕生,李效忠(蚌埠高等专科学校)(合肥工业大学)为了求已知矩阵人的秩和它的行空间的一个基,我们总是使用矩阵的初等行变换把A变成阶梯形矩阵,该阶梯形矩阵的非零行的个数即为矩阵A的秩,而该阶梯形矩阵的各非零行则构成矩阵月的行空间的一...  相似文献   

8.
王卿文 《数学杂志》1996,16(2):157-162
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   

9.
给出更多的对于给定行和向量存在(0,1)对称矩阵的等价条件,同时也讨论了(0,1)规范矩阵的情形.  相似文献   

10.
求矩阵A^+的初等变换法   总被引:1,自引:0,他引:1  
求矩阵A~+的初等变换法赵昌成(湖北郧阳师专441900)设A是复m×n矩阵,如果n×m矩阵X满足(1)AXA=A(2)XAX=X;(3)(AX)=AX;(4)(XA)=XA.则称X为A的More-Penrose广义逆(号表示对矩阵取共轭转置运算)....  相似文献   

11.
In this paper, by using global bifurcation theories we obtain some results for structure of positive solution set of some nonlinear equations with parameters. As a result, we obtain some existence results for positive solutions of the nonlinear operator equation. The main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinearities are positone.  相似文献   

12.
Quantale矩阵的广义逆及其正定性   总被引:2,自引:0,他引:2  
给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.  相似文献   

13.
Input-to-state stability (ISS) analysis and stabilization are concerned in this paper for switched nonlinear positive systems (SNPS), where the deterministic and random switching are both included. For general SNPS, switched affine nonlinear positive systems (SANPS) and switched linear positive systems (SLPS) with deterministic and some kinds of random ”slow” switching, some criterions on ISS are provided. From the criterions for SANPS and SLPS, the ISS properties can be judged just by the differential, algebraic and switching characteristics of the systems. Further, based on the criterions for SANPS and SLPS, some state feedback controllers are designed such that the closed-loop systems be positive, ISS or ISS in some stochastic senses. Four simulation examples verify the validity of our results.  相似文献   

14.
首先使用全局分歧理论得到了含参数非线性算子方程解集无界连通分支存在的结果,然后根据算子的正连通性得到了一类非正非线性算子方程正解的存在结果.使用本文的主要结果在无需假设非线性项为正的条件下可以得到某些微分边值问题正解的存在结果.  相似文献   

15.
16.
In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions.  相似文献   

17.
含参数泛函微分方程概周期正解的存在性   总被引:1,自引:0,他引:1  
研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.  相似文献   

18.
In this paper, we mainly focus on new inclusion sets for eigenvalues of a tensor. First, we propose new inclusion sets for eigenvalues of a tensor, which are sharper than some existing inclusion sets, and obtain the law of distribution of the number of eigenvalues for a tensor. Second, two new classes of tensors are introduced. Third, some bounds on the spectral radii for nonnegative tensors are given. Fourth, some checkable sufficient conditions for the positive definiteness (positive semidefiniteness) of some classes of even-order real symmetric tensors are obtained.  相似文献   

19.
In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.  相似文献   

20.
In this paper we study some particular solutions of Douglas type equations by means of generalized inverses and angles. We apply this result to characterize positive solutions and some special projections which are symmetrizable for a semidefinited positive bounded linear operator.  相似文献   

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