矩阵的矩阵

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。

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

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及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)。

But these methods limited by the expense of computing fundamental matrices and trifocal tensors or of the nonlinear optimization involved in computing epipolar tangencies. Through the studies of the invariants of the single axis motions, computational theories have been developed in this thesis to provide practical solutions for the problem of structure and motion from fitting the corresponding points in the whole sequence to its conic locus or conics for short.

在最近的研究中，一些研究人员利用视觉几何的方法从非定标的图象中对单轴旋转运动进行分析，提出了利用基本矩阵和三焦距张量求解单轴旋转运动中的关键参数——旋转角度的算法，但是该算法需要计算一系列相邻2图象的基本矩阵和一系列相邻3图象的三焦距张量，由于每个基本矩阵的自由度为7，每个三焦距张量的自由度为18，导致算法参数数量非常之大。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

The analytical solutions for the ABCD matrices of uniform transmission lines are expanded into matrix infinite series with very simple terms, from which two important properties about the time-domain response of all kinds of transmission lines are obtained. The lines analyzed may have frequency-dependent parameters and arbitrary terminals.

由于网络理论中ABCD矩阵的特殊性质，该方法对非均匀传输线时域响应的分析具有更大的优越性，能分析的传输线可以具有频变参数和任意负载终端，给出了计算非均匀传输线ABCD矩阵的两种方法，一种是将非均匀传输线等效为一系列由长度很短的均匀传输线构成的子网络的级联，另一种是用单步法直接求解ABCD矩阵所满足的微分方程。

At last, the Double Message Signal is proposed and the non-interfere condition is presented that the steering vectors are orthogonal in the weighted inner product space, with the inverse matrix of background covariance as the weighting matrix. The optimal polarization states are designed, according to the EM background.

最后，提出了一种双信息信号传输的方案并导出了无互扰传输的充要条件：两期望信号的信号矢量在以干扰噪声协方差矩阵的逆矩阵为加权矩阵的加权内积空间中正交，在给定的电磁环境下设计了双信息信号的极化状态。

In this paper, a class of matrix equation AXB = C is discussed.

中文摘要：本文针对一类一般意义下的矩阵方程，即AXB=C，应用矩阵分块的技巧，并结合特定矩阵的结构特征，采用合适的分解方法，给出了它有双对称，双反对称解的充要条件以及在条件满足时的通解表达式，并给出了各自在不同情况下的最佳逼近解。

The former firstly establishes state graph of power system, and then, with the use of the adjacency matrix and path matrix of the directed graph, fast finds out the key transmission sections suffering greatly from the outages of overload lines through simple calculation of matrix.

前者根据实时网络拓扑结构和潮流分布状态，在对初始电力网络简化、分区的基础上，利用有向图的邻接矩阵与路径矩阵，通过简单的矩阵运算，快速识别出与过载线路相关的关键输电断面；后者直接利用系统各支路的阻抗，从图论算法的基本思想出发，搜索最易遭受大负荷转移的关键传输路径，从而将安全性分析目标从整个网络缩小到某些关键的输电线路。

The former firstly establishes state graph of power system, and then, with the use of the adjacency matrix and path matrix of the directed graph, fast finds out the key transmission sections suffered greatly from the outages of overload lines through simple calculation of matrix. In the latter, the minimal short transmission path, the length of which is calculated with line impedance, is determined with graph theory to focus on security analysis objects from the whole network to some key transmission lines.

前者根据实时网络拓扑结构和潮流分布状态，在对初始电力网络简化、分区的基础上，利用有向图的邻接矩阵与路径矩阵，通过简单的矩阵运算，快速识别出与过载线路相关的关键输电断面；后者直接利用系统各支路的阻抗，从图论算法的基本思想出发，搜索最易遭受大负荷转移的关键传输路径，从而将安全性分析目标从整个网络缩小到某些关键的输电线路。

First we construct a covariance matrix from sample images, then compute the eigenvalues and corresponding eigenvectors of the covariance matrix, construct a feature matrix with the eigenvectors. Then every images in database can be projected into the feature matrix and gain a projection vector, so does the input image. Then we can judge the resemblance between input image with each image in database by computing the distance between their projection vectors.

我们首先根据采集的样本图像构造一个协方差矩阵，然后求取该矩阵的特征值，以这些矩阵特征值对应的特征向量构造出一个特征空间，然后将输入图像向该特征空间映射，将获取的映射系数与样本库中图像的映射系数进行距离计算，根据计算出的距离判定输入图像与样本图像间的匹配程度。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。