矩阵的矩阵

The algorithm uses the wavelet decomposition and reconstruction in multi-resolution editing B-spline curves and transforms a zonal matrix or sparse matrix to a row simplified matrix using the properties of the augmented matrix of the system of linear equations,which is a zonal matrix or sparse matrix,by elementary row operation.

该算法利用方程组的增广矩阵为类带状矩阵或者稀疏矩阵这一特点，运用简单的矩阵的行初等变换，将类带状矩阵或者稀疏矩阵化成容易接受的行简化矩阵，解方程组，使小波分解与重构的过程快速准确，使从事相关工作的技术人员更容易理解和接受。

This dissertation puts forward a structuring method of some complicated problems as well as methods of combination of the judgment matrix on group decision basis demonstrates that these two ways strengthen the consistency of the judgment matrix. Besides, it makes some researches into theory of combination of judgment matrix on the group decision basis, suggests two methods of calculating the coefficient of the convex combination and puts forward a method to construct individual and comprehensive judgment matrix based on rough-set by cooperating with others accordingly.

5给出了群决策条件下复杂问题结构化方法；提出了群决策条件下群体AHP判断矩阵集结的两种方法，证明了这两种集结方法保持或改善了判断矩阵的一致性；研究了群决策条件下判断矩阵优化集结原理，给出了判断矩阵两种凸组合系数优化计算方法；合作提出了一个基于Rough Set的个体判断矩阵和综合判断矩阵构造方法。

The third part is the judge method and its improvement method of a piece matrix is a diagonally dominant matrix: By using the Schur repair property of matrices, gives the sufficient and necessary conditions to judge a piece matrix be a diagonally dominant matrix.

第三部分为分块广义严格对角占优矩阵的判定方法及其改进：利用矩阵Schur补的性质，给出判定分块广义严格对角占优矩阵的充要条件，并利用逐次降阶的方法，使一个任意阶矩阵A逐次降为只需要利用定义判定一个矩阵是否满足要求，从而判定A是否是广义严格对角占优矩阵。

Topology information of network structure was also ohtained through converting an incidence matrix into standard triangular matrix.

网络关联矩阵经过矩阵变换形成三角矩阵，可以反映网络拓扑结构；对三角矩阵进行分级和分解运算，可以提取网络的拓扑信息。

In chapter one,we discuss tournament matrices that can not end in tie and theyare(0,1)-matrices,we first obtain a better lower bound for the number of regulartournament matrices,then we discuss the payoff matrix of tournament matrix,obtainsome properties of positive tournament matrices,a correlation between the spectralof a tournament matrix and its payoff matrix.We find serveal conditions that areequivalaent to a tournament matrix having 1 as its a eigenvalue.

第一章讨论不允许平局的竞赛矩阵-（0，1）-矩阵，得到了正则竞赛矩阵数目的一个下界，它改进了文献〓中已有的结果；在文献〓的基础上进一步讨论了正竞赛矩阵的性质，给出了利用已知平衡向量构造新平衡向量的方法；讨论了竞赛矩阵和它的支付矩阵的特征值之间的关系；指出了文献〓中的一个错误，回答了文献〓中的一个公开问题，得到了整数1为竞赛矩阵的特征值的充要条件及这种矩阵的谱根与得分向量之间的关系。

SVD is the general method for linear decomposition of a matrix into independent principal components, and is a form of Eigenvalue-Eigenvector analysis or principal components decomposition and, in a more general sense, of multi-dimensional scaling.

SVD分解根据矩阵的运算计算出矩阵的奇异值，然后根据奇异值计算出矩阵的两个奇异矩阵，将矩阵分解为三个矩阵的乘积形式。

Then, by constructing and analyzing the deviation matrix, computational way of adjusting the reciprocal judgement matrix into the satisfying consistency was proposed.

首先，给出了关于互补判断矩阵及其满意一致性的定义，同时还通过建立可达矩阵给出了互补判断矩阵满意一致性的判定方法；然后通过构造和分析一种偏差矩阵，给出了将互补判断矩阵改进为满意一致性矩阵的计算步骤。

In section 3, on the base of the iterative algorithm, we obtain a new iterative algorithm which is convergent to the signal faster than the old one. In section four, if the form of φ is simple and the sampling set is the integer set Z, then a direct reconstruction formula is presented.

在第二节，我们通过计算对偶框架来重建信号，这与传统的计算对偶框架方法不一样，该算法是通过计算一个矩阵的逆矩阵来计算对偶框架，当矩阵是奇异矩阵时，可通过奇异值分解方法或截断奇异值分解算法来求矩阵的广义逆矩阵。

In this paper, we first introduce the concepts and structures of generalized per-symmetric matrix, generalized centro-symmetric matrix or generalized bisymmetric matrix.

本文介绍了广义广对称矩阵、广义中心对称矩阵以及广义双对称矩阵的概念及结构，研究了这些特殊矩阵集合中，矩阵方程AXB=C及矩阵方程组A_1XB_1=C_1，A_2XB_2=C_2的迭代解法，同时考虑了相应的最佳逼近问题。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

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。