查询词典 diagonally dominant matrix

In chapter three, at first we introduces two kinds locally double αdiagonally dominant matrix from the concept of αdiagonally dominant matrix, by using this conception and the properties of αdiagonally dominant matrix and the techniques of inequalities, we discuss the relation of locally double αdiagonally dominant matrix and generalized strictly diagonally dominant matrix, according to these relations we obtain some effective criteria for generalized strictly diagonally dominant matrix.

在第三章中，首先由α-对角占优矩阵的定义，引进了两类局部双α对角占优矩阵，并利用它们及α-对角占优矩阵的性质，结合放缩不等式的技巧，讨论了局部双α对角占优矩阵与广义严格对角占优矩阵的关系，并由此得到判定广义严格对角占优矩阵的几个实用准则。

Therefore, in order to offer reference to readers, the paper systematically expound and prove the eigenvalue of special matrix that base on idempotent matrix, antiidempotent matrix, involutory matrix, anntiinvolutory matrix, nilpotent matrix, orthogonal matrix, polynomial matrix, the shape of , matrix, diagonal matrix, invertidle matrix, adjoint matrix, similar matrix, transposed matrix, numerical matrix, companion matrix, and practicality and superiority of the achievement was showed by some examples.

为此本文系统地阐述幂等矩阵，反幂等矩阵，对合矩阵，反对合矩阵，幂零矩阵，正交矩阵，多项式矩阵，形为：，矩阵，对角矩阵，可逆矩阵，伴随矩阵，相似矩阵，转置矩阵，友矩阵一系列特殊矩阵的特征值问题并加以证明，并通过一些具体例子展示所得成果的实用性和优越性。

In chapter one, firstly, we introduce the properties of αdiagonally dominant matrix and some exists determination conditions of generalized strictly diagonally dominant matrix, then we give some new results for the criteria of generalized strictly diagonally dominant matrix, finally, we show the validity of these conclusions.

在第一章中，首先引述了α-对角占优矩阵的性质及已有的一些判定条件，给出了判定广义严格对角占优矩阵的几个新的结论，最后说明了这些结论的有效性。

The second part is the judge method and its improvement method of a matrix is a diagonally dominant matrix: Introduces some basic methods to judge a matrix be a diagonally dominant matrix .Gives some improvement methods, and some number examples.

第二部分为广义严格对角占优矩阵的判定方法及其改进：介绍判定广义严格对角占优矩阵的一些基本方法，给出一些广义严格对角占优矩阵判定方法的改进，并给出数值例子。

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。

If A∈Rn×n is a L-matrix,and A isn't a diagonally dominant matrix,then some properties of the quasi diagonally dominant matrix with chain of non-zero elements were given.

对角占优矩阵、拟对角占优矩阵、H-矩阵等特殊矩阵在许多工程领域中起着很重要的作用，吸引了许多数学工作者对它的性质进行研究[1-5]。

In this paper, firstly, not only the incidence matrix ,adjacent matrix, cycle matrix, cut-set matrix of an undirected graph are summarized, but also the close contact between a graph and its corresponding matrix are discussed ; secondly, many problems of a graph which are solved by analysing its matrix are listed as follows:1、The co-tree set of a graph is obtained by using its cycle-matrix ; 2、The branches of its spanning tree are given by using its cut-set matrix ; 3、By making use of the incidence matrix of a graph ,not only its vertex cut 、cut vertex 、isolated point and spanning tree can be obtained ,but also the two sides which are whether parallel or not can be judged ;4、By using their adjacent matrix ,the two graphes which are whether isomorphous or not can be judged; once more, there is a detailed introduction in view of special graph (for example: bigaritite graph ,regular graph and so on);last but not least, a graph method of calculating the N power of a matrix is given and the practical applications of the theorem for degree is indicated.

本文首先综述了无向图的关联矩阵，邻接矩阵，圈矩阵，割集矩阵以及图和它对应矩阵之间的关系；其次总结出了利用上述各类矩阵可以解决的图的若干问题：1、利用图的圈矩阵可以求其连枝集；2、利用图的割集矩阵可以求其生成树的树枝；3、利用图的关联矩阵不仅可以求其割点、点割集、连通度、孤立点和生成树，而且可以判断两条边是否平行；4、利用图的邻接矩阵可以判断两个图是否同构；再次，针对特殊图（例如：二分图、正则图等等）的邻接矩阵作了详细介绍；最后，得到了利用图计算矩阵的N次幂的方法，指出度数定理的实际应用。

Examples illustrate that some special properties of the diagonally dominant matrix with chain of non-zero elements probably doesn't come into existence for quasi diagonally dominant matrix with chain of non-zero elements.

譬如目前关于拟对角占优矩阵的判定定理就有数十条之多[6-7]，至今仍有许多相关结论发表，其中杨志明[1]给出了拟具非零元素链对角占优矩阵的定义，并就这类矩阵的特征值的分布情况进行了讨论。

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。