M_3(F_p)的拟相合分类

基于有限结合环同构分类之需,在本文中我们定义了方阵之微别于相合关系的拟相合关系,决定了素域 F_p 上3×3方阵的拟相合分类,并举出了一个全体代表团.     

正定方阵的张量积

给出了正定方阵的合同根概念，并利用它，刻画了多个正定方阵的张量积仍为正定方阵的充要条件．     

Banach空间中线性算了的带W-权Drazin逆的逼近方法

1 引言 1958年Drazin首先引进了在可结合环和半群上一种拟逆的概念,后来人们就把这种拟逆称为Drazin逆。以后又对方阵的Drazin逆作了进一步的研究,并把它应用于Markov过程、线性微分方程组、差分方程组和最优控制等方面。1980年Cline和Greville提出了长方阵的带权Drazin逆的概念。     

方陣相似标准形

关于复数域中方阵的相似标准形问题,一般的线性代数教程中都采用以下两种处理方法。一种是几何的方法,即考虑线性变换的根子空间分解与循环子空间分解。本刊1964年第9期所载H.Reichardt一文,即属于此一类型。另一种是先建立多项式系数矩阵的相抵分类理论,然后再在这个基础上导出复方阵的相似标准形。从教学的角度看来,此二种讲法各有其不利之处。前者较抽象,不易为初学者所掌握,目前教学中已很少采用。后一种讲法有一系列的好处,但仍嫌不够直接,使初学者得到由远及近的感觉。考虑到开始讲授方阵相似分类问题之前,学生已经学过短阵相抵、对称方阵相合等问题,对方阵的初等     

拟变分不等式解集的极小本质集及应用

引入了拟变分不等式解集的极小本质集的概念，并证明了每个拟变分不等式(满足一定条件)的解集至少存在一个极小本质集．作为应用，还证明了大多数(在Baire分类意义下)拟-似变分不等式问题的解集是稳定的；每个拟-似变分不等式(满足一定条件)的解集至少存在一个本质连通区．     

也谈方阵的平方根

文[1]讨论了二阶方阵的平方根和三角方阵的三角平方根问题，但其结论有误．这里指出其错误并给出正确的定理．定义1设A是一个n阶方阵，若存在n阶方阵B，使B2=A，则称方阵B为方阵A的平方根．若有Bm=A，则称B为A的m次方根．文[1]给出如下定理：上（下）三角方阵存在上（下）三角方阵的平方根．对上述定理，文[1]没有给出一般证明，仅以三阶上三角方阵为例来证．但可惜的是，即使这样一个特殊情况的证明仍有漏洞，结论并不成立．例如不存在上三角方阵的平方根．事实上，对任意上三角方阵可以验证，均不存在上三角平方根．我们有如下定理：…     

关于反循环矩阵的对角化问题

反循环矩阵是一种特殊类型的矩阵，它本身有许多重要的性质，而且与矩阵的对角化问题有联系．本文拟探讨反循环矩阵的对角化问题，以及任一ｎ阶方阵Ａ可对角化时，Ａ与反循环矩阵之间的关系．     

拟似然非线性模型中MQLE的弱相合性的充分条件

拟似然非线性模型包括广义线性模型作为一个特殊情形.给出了拟似然非线性模型中极大拟似然估计的弱相合性的一些充分条件,其中矩的条件要弱于文献中极大拟似然估计的强相合性的条件.     

固定设计情形下回归函数小波估计的泛相合性

本文引入固定设计情形下回归函数小波估计的泛相合性概念，证明了此小波估计的泛相合性。     

二阶方阵的平方根和三角方阵的三角平方根

二阶方阵的平方根和三角方阵的三角平方根胡结梅（南昌航空工业学院基础一部３３００３４）定义设Ａ是一个ｎ阶方阵，若存在ｎ阶方阵Ｂ，使Ｂ２＝Ａ，则称方阵Ｂ是方阵Ａ的一个平方根．以ｄｅｔＡ表示方阵Ａ的行列式，则由定义得：ｄｅｔＢ＝±ｄｅｔＡ．下面的定理１给出...     

Principal powers of matrices with positive definite real part

We study principal powers of complex square matrices with positive definite real part, or with numerical range contained in a sector. We extend the notion of geometric mean to such matrices and we establish an operator norm bound in this context.     

Classification of Non-symmetric Sturm-Liouville Systems and Operator Realizations

The main objective of this paper is to give a classification of Sturm-Liouville differential equations with non-symmetric matrices coefficients in terms of the number of square integrable solutions of the system and its conjugate system. The conjugate system is innovatively introduced to get the classification. Furthermore, the asymptotic behavior of elements in the maximal domain is studied. As applications, the J-self-adjoint operator realizations are given for a special case in the classification.     

Core–EP inverse

In this work, we introduce a notion of ‘core–EP inverse’ for a square matrix which is not essentially of index one. This extends the notion of ‘core inverse’, which was initially defined for the matrices of index one. The properties of matrices having ‘core–EP inverse’ and ‘core–EP generalized inverse’ are studied, and obtained a formula to compute the core–EP generalized inverse from a particular linear combination of minors of given matrix.     

Hadamard matrices with few distinct types

The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. In this paper, we investigate Hadamard matrices with few distinct types. Among other results, the Sylvester Hadamard matrices are shown to be characterized by their spectrum of types.     

Maximum and minimum weighted diagonal sums of certain non-negative matrices

This paper extends the notion of diagonal sums of a square matrix to “weighted diagonal sums”. Using simple probabilistic arguments, most of the results of Wang [5] concerning the maximum and minimum diagonal sums of doubly stochastic matrices are extended to maximum and minimum weighted diagonal sums of stochastic matrices (Sec. 3). Two stronger versions of one of Wang's conjectures are also proven (Theorems 4.1 and 5.1), of which the latter easily generalizes to the case of non-negative matrices (Theorem 5.2). The paper ends with a few open questions and counter-examples.     

Partial matrices all of whose completions have the same spectrum

We characterize the square partial matrices over a field all of whose completions have the same spectrum, and determine the maximum number of indeterminates in such partial matrices of a given order as well as the matrices that attain this maximum number.     

Relative eigenvalue and singular value perturbations of scaled diagonally dominant matrices

The paper derives improved relative perturbation bounds for the eigenvalues of scaled diagonally dominant Hermitian matrices and new relative perturbation bounds for the singular values of symmetrically scaled diagonally dominant square matrices. The perturbation result for the singular values enlarges the class of well-behaved matrices for accurate computation of the singular values. AMS subject classification (2000)  65F15     

First-order polynomial differential equations over matrix skew series

In this paper we prove that one can reduce the solution of first-order polynomial matrix ordinary differential equations to the integration of similar scalar equations, provided that equation parameters are triangular. We establish requirements to elements of the desired matrix in the case when its parameters are double diagonal matrices. We consider the Riccati equation over the set of third-order square matrices. The obtained results are formulated in terms of “skew series”, the notion of which was introduced by us earlier.     

From Gårding’s Cones to p-Convex Hypersurfaces

We consider cones discovered by Gårding in 1959. They play the fundamental role in the modern theory of fully nonlinear second-order partial differential equations. A new classification of symmetric matrices is presented based on the m-positiveness property. Such a classification establishes a new trend in geometry, generating a notion of m-convex hypersurfaces.     

整数环上矩阵平方和的两个新结论

本文利用 F2 上方阵为平方矩阵的充要条件 ,证明了 :1任一阶数为偶数的整数矩阵可表示成 5个平方次幂整数矩阵之和 ;2任一整数矩阵可表示成 6个平方次幂整数矩阵之和 ,从而改进了文 [2 ,3 ]的主要结论 .