关于分块反循环矩阵及其对角化的讨论

本文给出了分块反循环矩阵的概念，讨论了含分块反循环矩阵的相似类，并且得知分块反循环矩阵一定与分块循环矩阵相似．     

分块矩阵的初等变换

本将矩阵的初等变换的概念推广到分块矩阵上并建立了计算分块矩阵的逆矩阵和分块方阵的行列式的若干简易方法。     

分块带状矩阵的逆

1引言如果分块矩阵A=(A_(ij))_(n×n)满足A_(ij)=O(j-i＞p且i-j＞q),其中A_(ij)为m阶矩阵,则称A为(p,q)-分块带状矩阵．分块带状矩阵在一些实际问题中经常出现,例如在量子场论中用途很广的非线性Schr(?)dinger方程的差分离散问题,解热传导问题等,都会遇到分块带状矩阵．常见的分块三对角矩阵,分块五对角矩阵都是特殊的分块带状矩阵．采用通常的方法求解分块带状矩阵的逆矩阵时,需要进行O(n~3)次m阶矩阵的运算．本文首先将分块带状矩阵扩充成可逆的分块上(下)三角矩阵,利用其逆矩阵导出了分块带状矩阵的逆矩阵表达式;进而利用所得到的公式分别推导了分块三对角矩阵及分块五对角矩阵的逆矩阵的快速算法,所需运算量为O(n~2)次m阶矩阵的运算．本文的结果扩充了文[1]等关于分块三对角阵求逆的相关结果．     

矩阵的分块初等变换与分块初等阵及其应用

讨论了矩阵分块初等变换和分块初等阵的定义和性质,利用这一工具研究了行列式的分块运算,分块矩阵的求逆和对称阵的分块合同变换等问题.     

不可约分块Hessenberg矩阵的逆阵

文[1]给出的非奇分块矩阵以分块三对角矩阵为其逆阵的充要条件,是该分块矩阵具有准三角性质,所谓分块矩阵R=[R_(ij)]的准三角性质,即R_(ii)非奇异并且     

一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质

本文给出一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质。     

关于分块极大极小矩阵性质的研究

利用矩阵分解、矩阵的Hadamard积和数学归纳法研究分块极大极小矩阵的性质.将极大和极小矩阵推广为分块极大和分块极小矩阵.在给出矩阵行列式、逆和特征多项式的同时,得到该类矩阵半正定的充要条件,还讨论了矩阵的无限可分性.     

矩阵分块方法的应用

矩阵的分块方法是矩阵论的一种重要方法,选择合适的分块方法可使一些证明变得简单明了.利用矩阵的分块方法给出关于矩阵的秩、特征多项式、行列式的若干等式、不等式及相关命题的简洁证明,有利于初学者理解和掌握.     

嘉量原理的分块摹矩阵连乘积表示

本文主要讨论分块摹矩阵（主要是含零子块较多的倩形）乘法运算的性质，分析了分块摹矩阵与赋嘉量有向图的关系，指出了嘉量原理如何用分块摹矩阵连乘积描述．     

关于K-分块循环矩阵及其对角化问题的讨论

给出了K-分块循环矩阵的概念,并探讨了K-分块循环矩阵的相似类及其对角化问题.     

Groups of Congruences and Restriction Matrices

Let be a domain of the Euclidean space R ^m sent onto itself by a finite group G of congruences. In this paper we first define M elementary restriction matrices related to the group G and to a system of irreducible matrix representations of G. We then describe a general procedure to generate M restriction matrices for any finite-dimensional space V() of real functions defined on , when V() is invariant with respect to G. The number M depends only on the group G. Restriction matrices for the space V() have a block structure and all blocks can be obtained as from an elementary restriction matrix. Restriction matrices related to V() define a decomposition of V() as the sum of M subspaces. Finally, owing to restriction matrices, we propose a result of decomposition for linear systems. Several examples are presented.This revised version was published online in October 2005 with corrections to the Cover Date.     

On rank variation of block matrices generated by Nevanlinna matrix functions

Within the framework of the multiple Nevanlinna–Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

对角因子分块循环矩阵的对角化和谱分解

导出了对角因子分块循环矩阵的概念，把循环矩阵的对角化和谱分解推广到具有对角因子循环结构的分块矩阵中去．     

分块友矩阵的相似类

定义了与n次矩阵多项式A(λ)友矩阵CA相似的矩阵为A(λ)的(广义)友矩阵,通过将此友矩阵分解成一组特殊的分块矩阵乘积的方法得到了一类(广义)友矩阵.     

Polynomial numerical hulls of matrix polynomials,II

In this article, we study some algebraic and geometrical properties of polynomial numerical hulls of matrix polynomials and joint polynomial numerical hulls of a finite family of matrices (possibly the coefficients of a matrix polynomial). Also, we study polynomial numerical hulls of basic A-factor block circulant matrices. These are block companion matrices of particular simple monic matrix polynomials. By studying the polynomial numerical hulls of the Kronecker product of two matrices, we characterize the polynomial numerical hulls of unitary basic A-factor block circulant matrices.     

两个分块矩阵相似性的研究

给出两个分块矩阵相似的两个充分必要条件 .也就是说 ,如果两个方阵 A和 B在 A2 =0和 B2 =0的条件下 ,则两个分块矩阵 A C0 B 和 A 00 B 相似的充分必要条件是 :rank A C0 B =rank(A) +rank(B)和 AC +CB =0 .如果两个方阵 A和 B在 A2 =A和 B2 =B的条件下 ,则两个分块矩阵 A C0 B和 A 00 B 相似的充分必要条件是 :AC +CB =C.     

Self-dual codes from orbit matrices and quotient matrices of combinatorial designs

In this paper we give constructions of self-orthogonal and self-dual codes, with respect to certain scalar products, with the help of orbit matrices of block designs and quotient matrices of symmetric (group) divisible designs (SGDDs) with the dual property. First we describe constructions from block designs and their extended orbit matrices, where the orbit matrices are induced by the action of an automorphism group of the design. Further, we give some further constructions of self-dual codes from symmetric block designs and their orbit matrices. Moreover, in a similar way as for symmetric designs, we give constructions of self-dual codes from SGDDs with the dual property and their quotient matrices.     

一类特殊的分块反循环矩阵的特征值问题

利用r-循环矩阵的基本性质,探讨了一类特殊的分块反循环矩阵的特征值问题．     

一类特殊的分块反循环矩阵的特征值问题(英文)

利用r-循环矩阵的基本性质,探讨了一类特殊的分块反循环矩阵的特征值问题.