特征值

QR algorithm is one of the major methods in computing the complete eigen-pairs of a dense matrix.

张昭 QR算法是目前计算满矩阵完全特征值组的最主要的方法之一。

This method combines the advantages of the QR eigenvalue algorithm and the Prony method. And

了QR特征值分析算法和Prony分析方法的优势，可以很容易在现有程序中实现。

The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided.

摘要研究具有无穷远零点的奇异H∞控制问题的二次矩阵不等式的可解性，证明了通过求解广义特征值问题，可以直接求得二次矩阵不等式的解，从而简化了原需通过复杂的系统分解和变换来求解二次矩阵不等式的方法。

The main topics are: determinants, matrices, rank of a matrix, vector spaces, linear equations, eigenvalues and eigenvectors, quadratics.

本课程的基本内容有行列式、矩阵、向量空间、线性方程组、矩阵的特征值与特征向量、二次型。

The purpose of this paper is to estimate the eigenvalues of square quaternion matrices.

估计定理，在估计定理的基础上提出了对角线元素是实数的四元数方阵的特征值。等式

The main topics are: determinants, matrices, rank of a matrix, linear equations, eigenvalues and eigenvectors.

本课程的基本内容有行列式、矩阵、线性方程组、矩阵的特征值与特征向量。

It shows that pair number of assignment eigenstructure"eigenvalue eigenvector" is less than or equal to rank of matrix E

研究表明：可配置特征结构的"特征值－特征向量"对数不超过阵

The algorithm makes iteration on the basis of rank of original matrix, and takes smaller memory of computer, and can save many computer hours. The advantages of the algorithm can be seen, especially for that only needing a few eigenvalues.

算法在原来矩阵阶数的基础上进行迭代，占用内存小，可以节省大量机时，尤其对于求解少数几个特征值的情况，更显示出算法的优越性。

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。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。