矩阵

In Chap 3, we give the definitions of left inverse and right inverse; present the fast algorithms of left inverse and right inverse for Toeplitz matrix, Hankel matrix, Loewner matrix and Vandermonde matrix with mxn order.

第三章先给出左逆及右逆的定义，然后分别给出了求m×n阶Toeplitz矩阵、Hankel矩阵、Loewner矩阵、Vandermonde矩阵的左逆及右逆的快速算法。

The classic iterative ones need special characters of the coefficient matrix; CG has over linear convergence, but the coefficient matrix is positive definite; Krylov subspace ones can deal with non-symmetric linear systems, but sometimes it must face"collapse"problems.

经典迭代法的收敛需要由系数矩阵的一些特定性质来保证；共轭梯度法具有超线性收敛性，但是系数矩阵必须是正定矩阵；Krvlov子空间法可用于非对称矩阵问题，但可能出现崩溃现象。

Lyapunov second method is applied to analysis of partial stability of equilibrium of linear ordinary differential equation with constant coefficients, the problems on partial stable matrix, partial positive definite matrix and Lyapunov matrix equation are studied.

将Lyapunov第二方法用于研究常系数线性系统零解的部分变元渐近稳定性，可引出相关的一些特殊矩阵问题，包括部分稳定矩阵、部分位正定矩阵、矩阵方程的可解性等。

Thisproblem is changed into the matrix approximation problem with matrix inequalities.Further, it is changed into the generalized eigenvalue problem with linear matrix in-equalities. In addition linear state feedback controller is designed.

先将最优控制问题转化为具有矩阵不等式约束的矩阵逼近问题，又转化为具有线性矩阵不等式约束的矩阵广义特征值最小化问题，从而设计了相应系统的线性状态反馈控制器。

By using matrix norm, matrix singular value, non-negative matrix theory, the regions of numaerical range and spectum of operator polynomial and the regularity of operator linear pencil are obtained.

8应用矩阵范数理论、矩阵的奇异值理论、非负矩阵的理论、友矩阵、算子的谱理论为工具，获得了算子多项式数值域具有的特性及其包含范围，算子多项式数值域与n-次数值域的关系，最后研究了算子线性束正则性的等价条件及谱分布情况。

A new method for consistency adjustment of fuzzy preference relations matrix in Group Decision is proposed.

针对模糊偏好关系矩阵本身是否一致，使得原矩阵渐进逼近目标矩阵的问题，提出了群决策中模糊偏好关系矩阵一致性调整的新方法。

In this paper,new quadratic PEk method and quadratic EPEk method are given for solving a system of linear algebraic equations whose matrix of coefficients is tridiagonal blocked matrix.

建立求解系数矩阵为分块三对角矩阵的线性代数方程组的新型二次PEk方法以及其外插迭代二次EPEk方法，对系数矩阵为对称正定矩阵情形，证明了新型二次PEk方法和二次EPEk方法的可解性和收敛性

To do so, Neo re-enters the Matrix. In his search for truth, he visits the Oracle the late Gloria Foster (news, protected by the fighter Seraph; rescues the Keymaker, who knows the system's weakness; encounters new foes in Merovingian, a Matrix political heavyweight, his duplicitous trophy wife, Persephone Monica Bellucci (news, and the Twins (English black-belt brothers Neil and Adrian Rayment), a silver-clad albino duo in dreadlocks; and finally encounters the Architect, the godlike creator of the Matrix.

为了了解这个，neo返回了矩阵；在他寻求真相的过程中，他拜访了先知，被战斗天使所保护的；救了持有钥匙的人，他知道矩阵系统的弱点；遇到了新的角色Merovingian，矩阵的政治上很有实力的人；他的妻子Persephone和新的双胞胎，银色的衣服；最终将遭遇到技师，象神一样的矩阵制造者。

Then, we set up the double-row monodromy matrix of the Hamiltonian, the transfer matrix and the reflection equation of the system with the help of the scattering matrix and the reflecting matrix.

接着借助量子反散射方法，运用两体散射矩阵和反射矩阵，构造了双行monodromy矩阵、转移矩阵和系统的边界反射方程，从而详细证明了系统的精确可解性。

In chapter three, in order to distinct N 0?matrices that defined by deferent references, we will use the following notions. A matrix is called N_0~2-matrix if the matrix is nonpositive and its all-principal minors are nonpositive.

不可约矩阵Perron余的Perron向量同原矩阵Perron向量有着继承性，另外非负矩阵的Perron余也可用于Perron根的估计，因此非负矩阵的Perron余的研究有着重要的理论价值。

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。