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The paper simplifies the joint diagonalization of matrices into optimization problem which only includes the eigen matrix. For solving the problem conveniently, each row vector of the eigen matrix is parameterized, then utilizes the improved genetic algorithm to get the optimal parameter.

摘要该文首先将矩阵联合对角化问题化简成一个只含有特征矩阵的优化问题，为了便于求解，文中将待求特征矩阵的每一列向量进行参数化处理，并利用改进的遗传算法寻找最优的新参数。

Starting from the securement problems in human realistic decision making, the concepts of the safety matrix, the safety index and the risk matrix are put forward in this paper.

本文从决策的现实特点出发，提出了安全矩阵、风险矩阵、安全指数等一系列概念；并进一步给出了在运用决策方法时考虑安全性的具体方法。

In this paper, a constructive proof of singular value decomposition of quaternion matrix is given by using the complex representation and companion vector of quaternion matrix and the computational method is described.

四元数矩阵的奇异值分解是四元数矩阵理论的重要内容，奇异值分解在四元数矩阵的理论研究和数值计算中都起到非常重要的作用。

This paper presents a new method of sparse matrix decompose which is based on the concept of matched degree, this method can make the process much simple and can be used in the decomposition of the construct matrix with multiple-freedom variables and constraints.

本文提出了基于匹配度计算的约束分解方法，采用这种方法，可以使约束分解的过程变得很简单，并可用于多自由度和多约束度变量的结构矩阵的分解。

This paper is mainly the dynamic input-output model that the time lag is one, which is base on the above models. After studying, we consider stochastic factor step by step in it, namely when consumption coefficient matrix is stochastic (when investment matrix is stochastic, it is almost same. So we dont research it), and they are both stochastic, then we research the stable increase solution. We utilize the means of the modern stochastic analysis and Markov process, that the stochastic dynamic input-output model don not exist the stable solution is proved. Namely, economic system must is adjusted constantly. The probability that the collapse time of the economic system is o is one.

本文对在上述基础上构造的一类时滞为1的动态投入产出模型，进行了深入研究，将随机因素逐步考虑进去，即对投入产出消耗系数矩阵为随机的情况(投资系数矩阵为随机的情况与投入产出消耗系数矩阵为随机的情况大致相同，这里就不再证明)，以及二者同时为随机矩阵时所得到的动态投入产出模型的稳定增长解问题，利用现代概率分析及马氏过程的工具，证明了不存在随机动态投入产出模型的稳定增长解；即投入产出模型反映的经济系统必须经常进行调整，其崩溃时间为无穷大的概率为零。

This paper first presents the definition of symmetric matrix and anti-symmetric matrix and then moves on the disscussion of certain properties of them.

本文先给出对称矩阵和反对称矩阵的定义，然后讨论了它们的若干性质。

In the paper, the kinds of reachability notions are defined and charactered firstly in their matrices and graphs. By the discussion of the matrix standard form and its transitive closure, the relation among the maximum partial reachability sets, the standard form of the matrix and its transitive closure are posted and the network partial reachability is based. The standard form provides methods for the improvement of the network reachability.

本文首先定义了诸可达概念及其等价刻画，通过布尔阵标准型及其传递闭包的讨论，揭示了网络极大局部可达集与矩阵标准型、传递闭包的关系，建立了网络局部可达的框架结构，并通过标准型为改善网络可达性提供方法。

In this paper, the theoretical analysis of matrix's triangular decomposition is mainly discussed, including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition,the necessary and sufficient condition of existence and so on.

本文主要对矩阵的三角分解理论分析作了比较全面的统述，它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件、存在性的充分条件等。

In this paper, we consider the following computing method of tridiagonal matrix:(1) decoupling of linear equation;(2) determination of determinant and eigenvalue-eigenvector relation;(3) matrix inversion.

二引宫在数值计算中，有许多问题足后归结为三对角矩阵的计算涸此研究它们的计算方法是有意义的。此外，有些三对角阵的计算方法可以做为带状阵计算的借鉴。

This paper focuses on the Schur theorem and the proof of it, the definition of a unitary matrix, Schur theorem given several important inference, and its application in the matrix above few examples.

本文重点研究了Schur定理的内容和它的证明，定义了酉矩阵，给出了Schur定理的几个重要推论，以及其应用在矩阵上面的几个实例。

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。