关于实方阵的正定性

本文研究一般实方阵的正定性 ,给出了方阵正定的一些充分必要条件     

非负定阵元素的扰动和正定完备化

在保持非负定性不变的前提下,本文对矩阵每一元素容许多大的扰动作了进一步的研究, 将本文的结论和C．R．Johnson提出的部分正定阵的正定完备化进行比较,容易发现对已知的正定矩阵求扰动,本文的结论比用C．R.Johnson的正定完备化计算扰动形式上更简单,同时也给出了不同于C．R．Johnson的部分正定阵的正定完备化表示的另外一个公式,推出了这些正定完备化矩阵应具有的若干性质．     

(N,1)-广义正定矩阵

本文对被屠伯埙称为亚正定的矩阵类进行了推广,即给出了(n,1)-广义正定矩阵的概念,进而得到了(n,1)-广义正定矩阵的一系列性质,最后将关于正定阵的Hadamard乘积的Schur定理及华罗庚定理推广到(n,1)-广义正定矩阵.     

Conditionally positive definite dot product kernels

This paper deals with conditionally positive definite kernels on Euclidean spaces. The focus here is on dot product kernels, that is, those depending on the inner product of the variables. Among the results, we include some properties relating conditional positive definiteness and standard convolution in the line and also results related to the characterization of the conditionally positive definite dot product kernels with respect to finite-dimensional polynomial spaces. We also introduce and characterize two large classes of strictly conditionally positive definite dot product kernels.     

关于正定矩阵的几个问题

本文推广了文［１］的主要定理，给出了用低阶矩阵判定高阶矩阵正定的判定定理，同时给出了矩阵方程ＡＸ＝Ｂ的反问题在正定矩阵类中解存在的充要条件及解的一般形式．     

流形上矩阵方程AX=B的正定及半正定阵的反问题

文[1-5]中研究了对称、对称半正定及流形上的对称半正定的反问题,并说明了其应用背景.本文研究线性流形上的正定及半正定阵的反问题,说明了文[1-3]中的一些结果为本文的特例.     

论正定列的一种扩张

设１，ｒ１，ｒ２，．．．ｒｍ，ｘ，１，ｒ１，ｒ２．．．，ｒｍ，ｘ，ｙ，ｙ∈（ａ，ｂ），ａ，ｂ，１，ｒ１，ｒ２，．．．，ｒｍ。     

一类二元n次型的正定性问题

本讨论了一类二元n次型的正定性问题，并且获得了它正定的一个充要条件。     

Hoeffding's inequalities: A counterexample

A sequence : ₀ satisfiesHoeffding's inequality of order n if wheneverX ₁,...,X _n are independent nonnegative integer-valued elementary random variables and are independent identically distributed nonnegative integer-valued elementary random variables, the common distribution of which is the average of those ofX ₁,...,X _n. We show that for each integerm greater than 2 there exists a sequence satisfying Hoeffding's inequality of every order greater thanm but not that of orderm. This answers a question raised by Berg, Christensen, and Ressel.     

Property T for Actions

We study property T for an action α of a discrete group Γ on a unital C*-algebra $$\mathscr{A}$$ . Our main results improve some well-known results about property T for groups. Moreover, we introduce Hilbert $$\mathscr{A}$$ -module property T and show that the action α has property T if and only if the reduced crossed product $$\mathscr{A}\;{\rtimes_{\alpha, r}}$$ Γ has Hilbert $$\mathscr{A}$$ -module property T.     

复正定矩阵的充要条件

本文研究Hermite正定矩阵、实正定矩阵的推广概念复正定矩阵,给出了复方阵复正定性的一些充分必要条件。     

一类广义正定矩阵的性质

广义正定矩阵有一系列推广,研究了一类广义正定矩阵,得到了这类广义正定矩阵的一些性质,并利用这些性质得到了这类广义正定矩阵的一些行列式不等式.     

泛正定阵与广义正定阵的关系

本文利用矩阵的稳定值,给出泛正定阵的等价条件,进一步得到泛正定阵与广义正定阵之间的一些关系．     

Positive definite dot product kernels in learning theory

In the classical support vector machines, linear polynomials corresponding to the reproducing kernel K(x,y)=xy are used. In many models of learning theory, polynomial kernels K(x,y)=_l=0^Na_l(xy)^l generating polynomials of degree N, and dot product kernels K(x,y)=_l=0⁺a_l(xy)^l are involved. For corresponding learning algorithms, properties of these kernels need to be understood. In this paper, we consider their positive definiteness. A necessary and sufficient condition for the dot product kernel K to be positive definite is given. Generally, we present a characterization of a function f:RR such that the matrix [f(xⁱx^j)]_i,j=1^m is positive semi-definite for any x¹,x²,...,x^mRⁿ, n2. Supported by CERG Grant No. CityU 1144/01P and City University of Hong Kong Grant No. 7001342.AMS subject classification 42A82, 41A05     

Strictly positive definite functions by integral transforms

We study the continuity and strict positive definiteness of positive definite functions on quasi-metric spaces given by integral transforms. We apply some of our findings to positive definite functions on the Euclidean space $R^m$ which are given by cosine transforms ($m=1$) and Fourier–Bessel transforms ($m>1$). We also apply the results to positive definite functions on a general quasi-metric space realized as extensions of certain real Laplace transforms defined by conditionally negative definite functions on the quasi-metric space itself.     

非自治系统渐近稳定的充分条件

本文对 Liapunov关于渐近稳定性的基本定理进行改进 ,在附加辅助函数前提下 ,同时放宽了 V正定 ,有无穷小上界 .V负定的条件 .改进了文 [1 ]～ [6]相应结果     

关于Hadamard乘积矩阵的一些性质的注记

对文 [1 ]的主要结论作了说明 ,给出 Hadamard乘积矩阵有关性质的更一般的结果 .     

An undecidable property of definite integrals

We show that it is undecidable whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic.

     

On positive definite solution of a nonlinear matrix equation

In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation X + A^*X^?αA = Q with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley & Sons, Ltd.     

有M P逆的Abel范畴中态射方程αxα*=β的非负定解

该文讨论了有M P逆的Abel范畴中态射方程αxα*=β的非负定解和正定解．作为其应用，给出了p 除环上矩阵方程AXA*=B的相关结果