矩阵代数

Linear algebra matrix multiplication is the most common operation, it is in scientific research and engineering development have a decisive role in raising the efficiency of its operations for many large academic research of the contents of papers here is to analyze the main two a matrix multiplication algorithm.

详细说明：矩阵乘法是线性代数运算中最常见的运算，它在科学研究以及工程开发中都具有举足轻重的作用，提高其运算的效率是很多大型的学术研究中的内容，这边论文是分析主要的两个矩阵乘法算法。

In the second part, we study the solution of some matrix equations in field theory and module theory,i.e., it is determined whether matrix equations have solutions in a field.

第二部分我们是通过代数的域论和模论来研究矩阵方程的解的问题，即判断一个矩阵方程在在域上是否有解。

They are presented in need of special curves and surfaces in engineering applications. In order to prove that the uniform C-B-spline basis is normalized totally positive, we compute the matrix which transforms the C-Bézier basis into the uniform C-B-spline and decompose this matrix into a product of. bidiagonal and stochastic factors.

本文用递推的方法，计算出代数三角空间中的n次C-Bézier基与n次均匀C-B-spline基之间的转换矩阵，并把该矩阵分解为一系列二对角阵的乘积，从而证明出n次均匀C-B-spline基是一个标准全正基，进一步用插入节点的方法，把它扩充为一组标准B基，从而我们可以利用B基的很多优良性质，在工程应用中对这两组基进行开发利用。

They are presented in need of special curves and surfaces in engineering applications. In order to prove that the uniform C-B-spline basis is normalized totally positive, we compute the matrix which transforms the C-Bézier basis into the uniform C-B-spline and decompose this matrix into a product of. bidiagonal and stochastic factors. Furthermore, we give a normalized B-basis by inserting knots.

本文用递推的方法，计算出代数三角空间中的n次C-Bézier基与n次均匀C-B-spline基之间的转换矩阵，并把该矩阵分解为一系列二对角阵的乘积，从而证明出n次均匀C-B-spline基是一个标准全正基，进一步用插入节点的方法，把它扩充为一组标准B基，从而我们可以利用B基的很多优良性质，在工程应用中对这两组基进行开发利用。

Matrix is the important in linear alyebra, and orthogonal matrix has a extensive applications in math and other subjects.

矩阵是线性代数中的重要内容，而正交矩阵在数学及其它学科中有着广泛的应用。

Considering the randomness of both elastic module and mass density of the structures, the element′s structural stiff and mass matrix have been built, the structure dynamic characteristics is analyzed based on probability, and the digit characteristics of natural frequency random variable is derived from the Rayleigh′s quotient.

利用随机因子法，建立了考虑结构弹性模量和质量密度同时具有随机性时结构的刚度矩阵和质量矩阵；从结构振动的瑞利商表达式出发，利用代数综合法推导出结构特征值随机变量数字特征的计算表达式。

In this dissertation, we establish the fundamental theory and methods to study systems of linear matrix equations over regular rings and polynomial rings over finite central algebras; and investigate some significant systems of linear matrix equations over the rings mentioned above.

本文在正则环和有限维中心代数上的多项式环上初步建立了研究矩阵方程组的基本理论和方法，并在上述环上研究了具体的具有重要意义的矩阵方程组。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

In this paper,lower bounds on the spectral radius of adjacency matrices of trees and perfect trees are discussed by algebraic method and edge switching of graph,and all trees which reach lower bounds on the spectral radius are obtained.

利用代数方法、图的边变换，以及树的邻接矩阵谱与L ap lacian谱的关系，研究树和完美树的邻接矩阵谱半径和L ap lacian谱半径的下界，给出达到下界的所有极树，得到的新结果改进了文献[2]的结论。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

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。