矩阵的矩阵

In this paper, the determinant and adjoint for a lattice matrix are studied, and some properties of the determinant and adjoint for lattice matrices are given.

研究了格矩阵的行列式与伴随矩阵，给出了它们的一些代数性质，同时给出了由一个格矩阵构造一个传递矩阵的方法。

Adjoint matrix of matrix plays an important part during the matrix theory.

矩阵的伴随矩阵在矩阵理论中有着重要地位。

In chapter 3, the paper proposed a new kind of preference relation, i.e. distance preference relation; followed this, a scale was introduced for constructing antisymmetric matrix, and consistency of the matrix was defined, three methods for computing priority vector were studied; At the end, two examples were used to demonstrate the application of the new method,and they showed that the introduction of antisymmetric matrix to AHP is effective and valuable.

本文首先对Saaty AHP的几种常见标度进行了比较分析，然后对正互反判断矩阵及模糊互补判断矩阵的权重计算方法进行了归纳和总结；最后，本文提出了一种新的偏好关系，即基于"差"的偏好关系，从而将反对称矩阵引入层次分析法，接着对新型偏好关系下判断矩阵的构造、一致性的定义与性质以及权重的计算方法做了初步的研究，最后用算例说明了新方法的应用，并做了相应的比较分析，结果表明采用基于"差"的偏好关系构造反对称矩阵拓展了AHP的应用范围，有一定的理论和应用价值。

This paper overviews the various algorithms for least square collocation, discusses the matrix QR decomposition, derives the relationship between QR decomposition and generalized inverse matrix, and obtains least square inverse used for calculating matrix. In addition, the estimation formula for least square collocation by QR decomposition and its accuracy formula are derived. A case study is conducted using gravity anomaly test and calculation to demonstrate that the QR method is correct and valid in least-square collocation calculation.

分析了目前采用的最小二乘配置法解算方法，在讨论了矩阵的QR分解方法的基础上，推导得出了矩阵QR分解与广义逆矩阵的关系，得出了可以直接利用QR分解求解矩阵的最小二乘逆，并推导了应用QR分解求解最小二乘配置的估值计算公式和精度估算公式，最后通过重力异常实例进行了计算，得出矩阵的QR分解用于最小二乘配置解算的正确性和可行性。

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

Zhan has determined the maximum and minimum numbers of positive entries of imprimitive irreducible nonnegative matrices with a given imprimitivity index. In this paper, we prove that if a positive integer is between the maximum and minimum numbers, then there exists an irreducible nonnegative matrix A with the given imprimitivity index and with the given number of positive entries.

非负矩阵是矩阵论中研究比较活跃的领域，不可约非负矩阵是比较重要的非负矩阵，本文分两部分，一部分主要在詹兴致教授的研究基础上研究了给定非本原性指标的不可约非负矩阵中非零元个数的连续性，肯定地回答了詹兴致提出的一个自然的问题。

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

This chapter defines the conceptsof P linear operator,〓 linear operator and 〓 linear operator by extending theconcepts of P matrix,〓 matrix and 〓 matrix to the linear operator from thelinear space of symmetric matrices to itself.In this chapter,we also present a path-following method and a potential reduction method for solving general linear matrixcomplementary problems,and analyzes their computational complexities undersuitable assumptions.

本章将第二章中给出的P矩阵、〓矩阵及P矩阵的概念推广到由实对称矩阵构成的向量空间到其自身的线性算子L上，得到了P线性算子、〓线性算子及P线性算子的概念，给出了求解一般线性矩阵互补问题的路径跟踪法和势函数约减法，并在L为P线性算子的假设下分析了这些算法的计算复杂性。

In this paper, the inertial theorem of real symmetric matrix has been proved by three methods in three aspects: the relationship between real symmetric matrix and real quadratic form, the relationship between real symmetric matrix and symmetric bilinear function of real linear space.

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度，介绍实对称矩阵的惯性定理的三种证明，以期加深对实对称矩阵的惯性定理的理解。

In this method the initial values of perspective projective matrix; rotative matrix and translative matrix are calculated from the fundamental matrix, than these matrices are optimized based on the coordinate value of corresponding points.

该方法从基本矩阵计算初始透视投影、旋转和竖直平移变换矩阵，然后以对应点坐标为基础对这些变换矩阵进行优化计算，从而有效地避免了优化计算的局部最小值，而且不过分依赖基本矩阵的计算精度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。