查询词典 involutory matrix

Through the definition of symmetric circulant matrix, the nature of the study, we discuss a class of n-order symmetric circulant matrix of eigenvalues and eigenvectors, and parity check on n different values are given for the matrix eigenvalue and the characteristics of vector formula.

通过对称循环矩阵的定义、性质的学习，我们讨论了一类n阶对称循环矩阵的特征值和特征向量，并分别就n取奇偶等不同数值时，给出了求该矩阵的特征值和特征向量的公式。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

This artic le researches a fast algorithm which extends the system matrix of JD into b lock circulant ma-trix,then uses block Fourier transform and block circulant matrix to perform matrix inversion and operation s.

提出一种快速算法，将联合检测的系统矩阵扩展成块循环矩阵，利用块FFT和块循环矩阵进行快速矩阵求逆和简化矩阵运算。

In view of practical problem during Sulige gas field development, this paper complete follow study content. Study material balance theory of two district compound gas reservoir. Carry out stress sensitivity experiment on matrix rock and labor created fracture core from Sulige gas field with America Core Company high pressure high temperature flow experimental instrument to study stress sensitivity change rule of different permeability matrix rock and created fracture core at the condition of time and again switch on and off well and different drawdown pressure. Carry out depletion experiment on matrix rock of different permeability serial combination with different kinds of allocation, using double core clamper serial connected experimental apparatus, to study gas well production performance of bi-zonal compound low permeability reservoir during low pressure production stage. At the basis of experimental study, establish single well simulation model to analyze development index infection caused by stress sensibility and production performance infection rule caused by inner formation and outer formation of bi-zonal compound gas reservoir permeability variation while considering stress sensitivity.

针对苏里格低渗气田开发中存在的实际问题，完成以下研究内容；研究了两区复合气藏物质平衡原理；利用美国岩芯公司高温高压流动实验仪，对取自苏里格气田基质岩芯和人工造缝岩芯进行应力敏感实验，研究不同渗透率基质岩芯和造缝岩芯在多次开关井和不同生产压差条件下的应力敏感变化规律；采用双岩芯夹持器串联实验装置，对不同渗透率串联组合的基质岩芯进行各种配产条件下的衰竭实验，研究两区复合的低渗储层气井在低压生产阶段的生产动态特征；在实验研究的基础上，建立单井模拟模型分析储层应力敏感性和非均质性对开发指标的影响，研究考虑应力敏感时两区复合气藏储层中内区和外区渗透率变化对开发动态的影响规律。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

A new fast algorithm of the minimal norm least squares solution for the linear system whose coefficient matrix is an m×n Loewner-type matrix with full column rank is given by forming a special block matrix and researching its triangular factorization.

通过构造特殊分块矩阵及其三角分解给出了求秩为n的m×n阶Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

Then the matrix Having these solution vectors as its column vectors is called a fundamental matrix for the system in Fundamental Matrix Solution Because the column vector .

则以这些解向量为列的矩阵被称为这个系统的基本矩阵。

In this paper, firstly the elimination tree theory is introduced in brief, and the structure of Jacobian matrix is determined by use of symbolic factorization; then by use of sparse vector method each column of lower triangular matrix L and each row of upper triangular matrix U are solved.

介绍了消去树理论，并采用符号因子分解技术确定雅可比矩阵的结构，然后采用稀疏向量法求取L阵的每行和U阵的每列。

This thesis has mainly contributed two results in theory: one is that the covariance matrix is not positive definitive if the number of sampling is least than the number of variables, the other is that the covariance matrix of discrete sample is positive definitive if and only if the sum of every random column vector of data matrix is non I-linear combination.

本论文在理论上，主要得出两个新的结果：ⅰ抽样调查中，若样本的个数少于变量的个数则样本协方差矩阵恒为非正定；ⅱ离散型样本协方差矩阵正定的充要条件是样本资料阵的各随机列向量是非I-线性组合。

However it can often be frust ating for a child when people are unable to pronounce their name.

但它往往可以令人沮丧的一个孩子当人们无法断言他们的名字。

All these compounds were obtained from this genus for the first time. Compound, 4-cumylphenol, was a new nature product.

所有化合物均为首次从本属海藻中分离得到，其中4cumylphenol为新天然产物。