矩阵

基本解释 (translations)

matrix  ·  matrices  ·  matrixes

与矩阵相关的网络例句 [注：此内容来源于网络，仅供参考]

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。

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。

The Matrix 矩阵矩阵矩阵矩阵 Some organizations fall somewhere between the fully functional and pure matrix.

一些组织介于纯功能和纯矩阵之间。这些组织被定义到项目管理知识手册里的第四版。

We call L n=1-matrices for N_0~1-matrices. Meyer introduced the concept of the Perron complement of a nonnegative and irreducible matrix in 1989 and used it to construct an algorithm for computing the stationary distribution vector for Markov chains. We extend the Perron complements of nonnegative and irreducible matrices to the Perron complements of nonpositive and irreducible matrices.

我们这里是把Perron余的概念推广到了非正不可约矩阵，显然它也具有非负矩阵相类似的性质，逆N 01矩阵又是特殊的非负矩阵，我们证明了在一定条件下，逆N 01矩阵和N 02矩阵的广义Perron余的继承性，并给出了相关的不等试：逆N 01矩阵和N 02矩阵的广义Perron余逆矩阵的不等式；逆N 01矩阵的主子阵与其逆矩阵的不等式。

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。

Selfconjugate matrix, skewselfconjugate matrix, perselfconjugate matrix, skewperselfconjugate matrix, centrosymmetric matrix, skewcentrosymmetric matrix, bisymmetric matrix, and skewbisymmetric matrix over a ring with an involutorial antiautomorphism are defined. Significant criteria for matrices to be bisymmetric and skewbisymmetric are obtained.

在具有对合反自同构的环上定义了自共轭矩阵，斜自共轭矩阵，广自共轭矩阵，斜广自共轭矩阵，中心对称矩阵，斜中心对称矩阵，双对称矩阵和斜双对称矩阵，建立了双对称矩阵和斜双对称矩阵的重要判定定理。

In this dissertation, we construct the Bariev model with nine kinds of boundary fields by the matrices K_± defining the boundaries. And then the Lax operator is given in the form ofmatrix, as well as the basic quantities, e.g., the R -matrix, the monodromy matrices and the transfer matrices are defined. By using the expression of the local Lax operator of the model,the action of the monodromy matrices T, T~(-1), U_ on the pseudo-vacuum state is given outin detail. Furthermore, the main fundamental commutation relations are obtained through the reflection equations, the recursive n-particle state as well as the one-particle exact solution is given and the Bethe ansatz equations are found accordingly. Finally, we list the nesting boundary K matrices, which play a crucial role for obtaining the n-particle solution and finding the Bethe ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum of the system by means of the nested algebraic Bethe ansatz method.

在这篇文章中，我们利用边界K_±矩阵构造出了具有九种边界场的Bariev模型，同时给出了该模型L算子的具体矩阵表示形式，并定义了R矩阵，monodromy矩阵以及转移矩阵；接着利用L算子的矩阵形式，给出了其对应monodromy矩阵T、逆矩阵T~(-1)作用到真空态上的值，并利用Yang-Baxter关系及反射方程得到了双行monodromy矩阵U作用到真空态上的值；然后利用反射方程通过复杂的计算得到了一系列重要的基本对易关系式，并给出了模型的递推的多粒子波函数、单粒子解及Bethe ansat方程；最后给出了模型的嵌套的边界K矩阵的具体形式，从而为运用嵌套Bethe ansatz方法求解该模型的多粒子解、Bethe ansatz方程以及系统的能谱打下了很好的基础。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

Thesis and mainly discuss the following problems:What we mainly discussed in the second chapter as follows:(1) S1,S2 are sets of symmetric orth-symmetric matrices;(2) S1,S2 are sets of bisymmetric matrices;(3) S1,S2 are sets of anti-symmetric orth-anti-symmetric matrices;(4) S1,S2 are sets of bi-anti-symmetric matrices;(5) S1 is the set of symmetric orth-symmetric matrices, S2 is the set of anti-symmetric orth-anti-symmetric matrices;(6) S1 is the set of bisymmetric matrices, S2 is the set of bi-anti-symmetric matrices;(7) S1 is the set of anti-symmetric orth-anti-symmetric matrices, S2 is the set of symmetric orth-symmetric matrices;(8) S1 is the set of bi-anti-symmetric matrices, S2 is the set of bisymmetricmatrices;On the base of studying the basic properties of the matrices, the expression of solutions and some numerical examples are presented.

本文第二章将主要就上述问题讨论如下几种情况： 1.S_1，S_2为对称正交对称矩阵； 2.S_1，S_2为双对称矩阵； 3.S_1，S_2为反对称正交反对称矩阵； 4.S_1，S_2为双反对称矩阵； 5.S_1为对称正交对称矩阵，S_2为反对称正交反对称矩阵； 6.S_1为双对称矩阵，S_2为双反对称矩阵； 7.S_1为反对称正交反对称矩阵，S_2为对称正交对称矩阵； 8.S_1为双反对称矩阵，S_2为双对称矩阵。

与矩阵相关的网络解释 [注：此内容来源于网络，仅供参考]

augmented matrix：增广矩阵

为了使用矩阵来解联立方程式系统,我们在此介绍增广矩阵 (augmented matrix) 以便使用矩阵去解决线性方程系统. 增广矩阵 是线性系统的系数矩阵 (9.5) ,在 (9.5) 的右边增加附加的一行. 以增广矩阵表示线性系统 (9.5) 为

matrix bookkeeping：矩阵簿记,矩阵簿记

matrix assessment 矩阵评价法,矩阵评价法 | matrix bookkeeping 矩阵簿记,矩阵簿记 | matrix calculation 矩阵计算

incidence matrix：关联矩阵

图的邻接矩阵是如下定义的:是一个的矩阵,即关联矩阵表示法是将图以关联矩阵(incidence matrix)的形式存储在计算机中.图的关联矩阵是如下定义的:是一个的矩阵,即弧表表示法将图以弧表(arc list)的形式存储在计算机中.

inverse matrix：反矩阵

迹数(trace),也就是对角线数据的总和,转置矩阵(Transpose Matrix),则是将矩阵数据列跟栏对调将横的数据变成直的,反矩阵(Inverse Matrix)它的定义为与目标矩阵相乘可以得到单位矩阵,为一个可逆矩阵.上面的结果用单纯的CV_LU是无解的,

matrix element：矩阵元素,矩阵元

matrix eigenvalue 矩阵特征值,矩阵特征值=>行列固有値 | matrix element 矩阵元素,矩阵元 | matrix equation 矩阵方程,矩阵方程

matrix norm：矩阵的模,矩阵的模,矩阵模,矩阵模,矩阵模量,矩阵模量

matrix multiplier 矩阵乘数,矩阵乘数 | matrix norm 矩阵的模,矩阵的模,矩阵模,矩阵模,矩阵模量,矩阵模量 | matrix notation 矩阵记号,矩阵符号,矩阵符号表示,矩阵运算

Singular matrix：奇异矩阵

SVD),可以说是对角化应用的特例,它具有与Eigen Value,Eigen Vector相同的特性,分解后向量的矩阵乘积可以还原为原矩阵,而他可以对奇异矩阵(Singular Matrix)做分解,亦可以对非奇异矩阵做分解.奇异矩阵的定义就是不能计算为反矩阵的矩阵,

Matrix Multiplication：矩阵乘法,矩阵乘法

matrix model 矩阵模型,矩阵模型 | matrix multiplication 矩阵乘法,矩阵乘法 | matrix multiplier 矩阵乘数,矩阵乘数

permutation matrix：置换矩阵

该文提出了一种基于置换矩阵(permutation matrix)的非规则低密度奇偶校验(LDPC)码构造方法. 首先,提出了基于改进eIRA(IeIRA)算法的全局矩阵;接着,通过对全局矩阵M进行矩阵置换,生成LDPC码的校验矩阵日;研究了校验矩阵H中短圈(short cycle)长度与置换矩阵循环移位系数的关系,

matrix, transpose：矩阵转置,矩阵换行,矩阵换列

matrix theorem 矩阵定理 | matrix transpose 矩阵转置,矩阵换行,矩阵换列 | matrix unit 矩阵单元