矩阵

In this paper, the determinant and adjoint for a lattice matrix are studied, and some properties of the determinant and adjoint for lattice matrices are given.

研究了格矩阵的行列式与伴随矩阵，给出了它们的一些代数性质，同时给出了由一个格矩阵构造一个传递矩阵的方法。

NMF can find basis vector through observation data,and discover image feature,obtaining the fusion image.

介绍了非负矩阵分解的基本思想，讨论了非负矩阵分解用于图像融合的可能性，并实现了基于非负矩阵分解的遥感SAR图像与SPOT图像的融合，NMF能通过观测图像数据找到图像的基矩阵，发现图像的特征，从而最终获得融合图像。

The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.

对矩阵A是非对称情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，并给出了其解的表达式，描述了求解问题的算法；讨论了带对称和双对称约束的总体最小二乘问题，利用Ricaati矩阵方程的理论得到了解存在的一个充分条件，分别对对称矩阵和双对称矩阵两种情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，给出了其解的表达式，提出了求解这些问题的算法，并给出了数值例子。

Meantime we also get the explicit construction of pseudo-inverses of bordered matrix and obtain many new results.

本章所使用的主要工具是QQ-SVD，其中在研究加边矩阵{1，3}-和{1，4}-逆时，又使用了构造特殊非奇异矩阵的技巧，给出了加边矩阵{1，3}-和{1，4}-逆的显示结构，并进一步得到了加边矩阵伪逆的显示结构，获得了许多新的结果。

Bordered matrix has very wide applications in the matrix theory, many specialists and scholars had studied bordered matrices before.

本节在P-SVD中通过构造特殊的非奇异矩阵，详尽地揭示了两个矩阵乘积{1，3}-和{1，4}-逆的结构，从而最终解决了两个矩阵乘积{1，3}-和{1，4}-逆的反序律，并得到了两个矩阵乘积伪逆反序律的一个新的等价性条件。

Rules for fusing, which specify the possible values of the charge that can be obtained when two particles of known charge are combinedbtogether, used for reading out information. In the #nu=5/2# FQH state, it can be realized by measuring whether each pair annihilates fully or not with interference experiment. The representation of the braid group realized by n anyons is cmpletely characterized by the R-matrix and F-matrix which satisfy a pentagon equation and a hexagon equation, coherence conditions for the corresponding anyon model.

满足一定的聚合规则，用于信息读取（在填充因子为5/2的分数量子霍尔效应中，可以通过干涉实验测量每对相邻的粒子相聚合的湮灭情况来实现信息读取）；N个任意子组成的体系的标准基中辫子群表示可以完全由R矩阵和F矩阵决定，不同任意子模型中的R矩阵和F矩阵的具体形式可以通过五边形和六边形方程求出。

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

The program is the main description of the matrix operations, including the basic matrix operations, matrix inverse, matrix singular value decomposition, and the characteristic value and characteristic vector solution and so on.

详细说明：该程序是主要描述的是矩阵运算，包括矩阵的基本运算，矩阵的求逆，矩阵的奇异值分解，以及特征值以及特征向量的求解等等。

He structure of Toeplitz matrix is special, Circulant matrix is one of a class of this special matrices since it's structure is more special.

oeplitz矩阵是一类结构特殊的矩阵，循环矩阵是其中结构更特殊的一类矩阵。

For problem II, many references have studied it and obtained its common solutions, symmetric solutions, skew-symmetric solutions and its optimal approximation constrained solution, but the representation of its solutions are complicated.

本文首次采用迭代法系统的研究了它求一般解、对称解、反求解约束矩阵方程及其最佳逼近的迭代法的研究对称解、中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解、对称次反对称解及其最佳逼近问题，并首次成功地解决了它求中心对称解、中心反对称解、自反矩阵解、反自反矩阵解、双对称解与对称次反对称解及其最佳逼近的问题，拓广和改进了已有的研究成果。

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。