矩阵代数

Linear algebra's adjoint matrix calculation of C language accompanying matrix definition : Matrix p...

线性代数之伴随矩阵计算C语言实现伴随矩阵定义：把矩阵所有位置上的元素替换为元素的代数余子式，即得原矩阵的伴随矩阵。

We find serval conditions that are equivalent to 2-tournament matrices being singular,give the bound for the maximum algebraic multiplicity of 0 as an eigenvaulle of n order2-tournament,obtion the spectral radius of a singular 2-tournament matrix of order nis bounded above by n-2,and investigate 2-tournament matrix achieving this bound.

第五章讨论了2-竞赛矩阵的奇异性和特征值之间的关系，得到了2-竞赛矩阵奇异的充要条件，给出了2-竞赛矩阵的零化向量的刻划，得到了得分向量，3-圈数目与奇异性的关系；给出了2-竞赛矩阵的特征值0的代数重数的上下界，得到了奇异的2-竞赛矩阵谱根的最大值及谱根达到最大值的竞赛矩阵的得分向量的特征。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

In chapter 3, the concepts of M-matrix and H-matrix over a commutative Banach algebra have been proposed, and some of their important properties and applications in linear systems over a commutative Banach algebra have been studied. For usual complex matrix, the Bellman inequality with Hadamard product has been proved.

第三章，提出了交换Banach代数上M一矩阵及H一矩阵的概念，研究了其一些重要性质，并给出了在交换Banach代数上线性系统中的应用；对有限维复矩阵，证明了关于 Hadamard乘积的 Bell.an不等式。

This thesis consists of two parts. The first one was that boundary value problem was discrete with five point difference method. Three kinds of memory formats were studied, which were full matrix, half band width and row compress sparse. Full matrix memory format and half band width memory format first was contrasted. The results show that half band width has efficiency in space. Then the algebraic system of finite element method was solved by Gauss-Seidel iteration method to popular row compress sparse memory format.

本论文由两部分组成，第1部分针对边值问题，用5点差分格式进行离散，并对离散矩阵这类大型稀疏矩阵，研究了系数矩阵的3种存储格式的优劣，即：满矩阵存储格式、半带宽存储格式和按行压缩稀疏存储格式，首先我们将满矩阵存储方式和半带宽存储格式进行了对比，迭代法的数值实验表明：利用半带宽存储的矩阵在空间运算方面具有高效性；然后针对目前数值实验中流行的按行压缩稀疏存储格式，实现了有限元离散代数系统的迭代法的求解。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

With proving the isomorph between the function matrix algebra systems and the Boolean algebra s disjunction-conjunction systems,a method of extending the function matrix is proposed,and the expanding theorem of the extended function matrix is proven.

提出了功能矩阵的概念，在证明功能矩阵的代数系统与布尔代数析取合取代数系统同构的基础上，对功能矩阵进行扩展，并证明了扩展功能矩阵的展开定理；利用扩展功能矩阵逐步展开与约简，实现了功能的求解算法。

This paper takes advantage of interval algebra and rectangle algebra theories. and brings forward a new reasoning method based on combination of the MBR model's cardinal direction relation and rectangle algebra relation; And provides the composing method based on the direction relation matrix by using the direction relation matrix to denote the direction relations between the objects'MBRs.

本文以物体的MBR为模型，利用区间代数及矩形代数理论，提出了一种基于MBR的主方向关系与矩形代数关系相结合的推理方法；同时利用方向关系矩阵表示物体MBR之间的方向关系，得到了基于方向关系矩阵的组合推理方法。

This direction of research associates the graph in graph theory with the matrix in algebra by the matrix representation of a graph, then studies the algebraic property of graphs with the methods in graph theory and algebra.

该研究方向是通过图的矩阵表示将图论中的图与代数中的矩阵联系起来，再利用图论和代数方面的一些方法来研究图的代数性质。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。