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The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

In chapter one, firstly, we introduced several kinds of diagonally dominant matrices definition and their connection. Secondly, the relationship between those kinds of matrices and the convergence of some basic iteration methods (such as Jacobi, Seidel and SOR iteration methods) are also mentioned.

第一章，我们先简介了几类对角占优阵的定义及它们之间的关系，并介绍了一些基本迭代法(指Jacobi，Seidel及SOR迭代法等)的收敛性与这些矩阵类的关系。

In addition, the connection of complex matrices and complex symmetric matrices , namely every complex matrix is similar to a complex symmetric matrix, is found.

另外，本文找出了复对称矩阵与一般的复矩阵的关系，即每个复矩阵都相似一个复对称矩阵。

These weight matrices are actually the least solution matrix and all maximal solution matrices of the min-implication fuzzy relation equation, respectively. The complete solution set of min-implication fuzzy relation equation can be determined by the maximal solution set of this equation.

同时给出了严格的定理证明：这些连接权矩阵分别为对应的最小-蕴涵合成模糊关系方程的最小解和所有极大解，从而得到了此模糊关系方程的完备解集。

Let Mn be the linear space of all n × n matrices over F,and let Sn be its subspace consisting of all symmetric matrices.

Mn记F上所有n阶矩阵构成的线性空间，Sn记F上所有n阶对称矩阵构成的线性空间。

We denote by M_n and T_n the space of n×n full matrices and the space of n×n upper trangular matrices over F, respectively.

设F是域。记M_n和T_n分别为域F上n×n全矩阵空间和n×n上三角矩阵空间。

And three main steps of all subspace algorithms are explored. First, using an LQ-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Next, the SV-decomposition of the projection is calculated to directly lead to the observability matrices and a Kalman filter estimation of the state sequences.

概括了子空间辨识算法的三个主要运算步骤：首先由LQ分解计算特定Hankel矩阵的行空间投影；再对该投影进行SVD，获取系统的可观测矩阵及状态序列的Kalman滤波器估计；最后由可观测矩阵和／或估计的状态序列确定系统矩阵。

For an arbitrarily time-varying system, a series of hankel matrices are established directly from the combined measurements of displacement, velocity and acceleration together with the input excitations, which have been obtained through only one experiment of the system. The varying equivalent state space system matrices of structures at each moment are then identified by singular value decomposition using the forced responses and input forces.

该方法以任意组合的位移、速度、加速度受迫响应信号为测量信息，仅利用一组输入、输出信号组成Hankel矩阵，通过奇异值分解的方法识别出等效状态的系统矩阵，然后运用推导出来的通用时变系统的转换矩阵，将等效状态系统矩阵转换成为实际物理状态下的系统矩阵，从而识别出实际系统的质量、刚度、阻尼矩阵。

In chapter 3, based on the relationship between the minimal eigenvalue and the spectral radius of non-negative matrices, we derive some others upper and lower bounds on irreducible M-matrices.

第三章利用M矩阵的最小特征值与非负矩阵谱半径之间的关系，给出了不可约M矩阵最小特征值上下界的几个估计式。

And the sufficient and necessary conditions are obtained and the uniqueness of T is discussed and an algorithm for solving the inverse problem is provided. The other kind of structure inverse eigenvalue problem is for unitary Hessenberg matrices with positive subdiagonal elements. That is, a unitary Hessenberg matrices with positive sub-diagonal elements can be constructed when its eigenvalues and the eigenvalues of H_(11) and H_(22) are known. Here H_(11) and H_(22) are rank-one modifications of k × k leading principal submatrix of H and of its × remain submatrix respectively. In the end, the uniqueness of H and an algorithm is obtained.

文中首先讨论了这三组特征值之间的交错关系，接着确定了该逆问题有解的充要条件，并论证了其解的唯一性问题，最后给出了相应的数值算法；本文第二个问题解决的是一类不可约的酉Hessenberg阵的逆特征值问题：即一个不可约的酉Hessenberg阵可以由它的特征值、它的前k阶秩一修正的顺序主子阵的特征值以及它的后n—k阶余子阵的秩一修正阵的特征值来确定，文中最后讨论了唯一性和相应的算法。

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This new product will become our best seller.

这个新产品会成为我们最畅销的产品。