矩阵的拟直和分解与Craig定理

讨论了矩阵的和与其加项之间,在等价关系及(对称阵的)合同关系上的联系.并进一步讨论了矩阵和的非零特征值与其加项的非零特征值之间的联系,给出了C ra ig定理的一个代数形式和代数证明.     

矩阵的满秩正交分解

旨在给出矩阵一种新分解(满秩正交分解).分解简单易求,且与矩阵的奇异值分解有类似的性质和应用.     

初等变换的一个应用:矩阵的满秩分解

给出利用初等变换求矩阵满秩分解的一个简洁方法.     

关于具矩阵三角分解修正拟Newton法的收敛性分析

本文对于Johnson、Austria提出的求解非线性方程组的基于矩阵三角分解修正的一类拟Newton法进行了改形,并给出了该算法的Kantorovich型的收敛性分析,从而完整了文(l]的收敛理论,亦为算法的初始选取,提供了依据.     

几类矩问题的矩阵解法

本文利用矩阵论的方法对讨论截断矩问题,无穷矩问题以及[带不等号的矩问题。     

拟酉矩阵与拟Hermite矩阵

利用次Hermite矩阵给出了拟酉矩阵与（反）拟Hermite矩阵的概念,研究了它们的基础本性质及其之间的关系,将各类酉矩阵与Hermite矩阵一了起来。     

Bell数的Hankel矩阵的一般表示

§ 1.　Introduction　　TheBellnumberBn countsthenumberofpartitionsofann set,withthefirstvaluesB0 =1 ,B1 =1 ,B2 =2 ,B3 =5 ,B4=1 5 ,B5=5 2 .ItsexponentialgeneratingfunctionisB(x) =∑n≥ 0Bnxnn ! =eex-1 ,(see [2 ]) .LetthegeneralhankelmatrixofBellnumberbe Bn(t) =Bt Bt+ 1 …Bn +tBt+ 1 Bt+ 2 …Bn+t+ 1…………Bn+t Bn+t+ 1 …B2n +t,(see [3]) .Recently ,AIGNER [1 ]obtaineddet Bn( 0 ) =det Bn( 1 ) =n ! ! ,wheren ! ! =∏nk =0 k ! .ThepurposeofthispaperistoprovideageneralrepersentationoftheH…     

由特征值唯一确定的实3×3Hankel矩阵(英文)

本文研究了由特征值唯一确定的3×3实Hankel矩阵.借助于M.Fielder[1]的结论并经过细致的讨论,得到3×3实Hankel矩阵由其特征值唯一确定的充分必要条件,刻画了3×3实Hankel矩阵的一种特征值性质.     

矩阵因子分解及其应用举例

通过矩阵方程定义了矩阵的左、右因子和双因子,给出了各类因子存在的充要条件,并将其应用到满秩分解和极分解等典型例子中.论证中,采用多种观点和方法,空间映射、矩阵运算并重.     

行(列)反对称矩阵的满秩分解和广义逆

本文研究了行(列)转置矩阵与行(列)反对称矩阵的性质.利用分块矩阵理论获得了许多新的结果,给出了行(列)反对称矩阵的满秩分解、秩分解和广义逆的公式及快速算法.它们可极大地减少行(列)反对称矩阵的满秩分解、秩分解和广义逆的计算量与存储量,并且不会丧失数值精度.     

Analysis of the Structured Total Least Squares Problem for Hankel/Toeplitz Matrices

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) approach when structured matrices are involved and a similarly structured rank deficient approximation of that matrix is desired. In many of those cases the STLS approach yields a Maximum Likelihood (ML) estimate as opposed to, e.g., TLS.In this paper we analyze the STLS problem for Hankel matrices (the theory can be extended in a straightforward way to Toeplitz matrices, block Hankel and block Toeplitz matrices). Using a particular parametrisation of rank-deficient Hankel matrices, we show that this STLS problem suffers from multiple local minima, the properties of which depend on the parameters of the new parametrisation. The latter observation makes initial estimates an important issue in STLS problems and a new initialization method is proposed. The new initialization method is applied to a speech compression example and the results confirm the improved performance compared to other previously proposed initialization methods.     

Finite Rank Hankel Operators over the Complex Wiener Space

This work studies finite rank Hankel operators H _b on a Hilbert space of holomorphic, square integrable Wiener functionals. The main tool to investigate these operators is their unitary equivalent representation on the Hilbert space of skeletons. The finite rank property is characterized in terms of a functional equation for the symbol b, which generalizes the well known equation b(z+w)=b(z)b(w). Also finite rank symbols of polynomial type are characterized in terms of their chaos expansions.     

Asymptotic Formulas for Determinants of a Sum of Finite Toeplitz and Hankel Matrices

The purpose of this paper is to describe asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices with singular generating functions. The formulas are similar to those of the analogous problem for finite Toeplitz matrices for a certain class of symbols. However, the appearance of the Hankel matrices changes the nature of the asymptotics in some instances depending on the location of the singularities. Several concrete examples are also described in the paper.     

Operators of Hankel type

Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered. The present note provides a parametric labeling of all the Hankel symbols of a given Hankel operator X by means of Schur class functions. The result includes uniqueness criteria and a Schur like formula. As a by-product, a new proof of the existence of Hankel symbols is obtained. The proof is established by associating to the data of the problem a suitable isometry V so that there is a bijective correspondence between the symbols of X and the minimal unitary extensions of V.     

关于除环上分块矩阵秩的等式

本文使用双矩阵分解方法研究除环上分块矩阵秩的等式,给出了Marsaglia-Styan公式一个新的证明并获得了一些新的秩等式的刻划.