正定矩阵

In chapter 2, we sets up the convergence theory of the alternating method for solving Hermitian positive definite systems of linear equations, and establishes the corresponding comparison theorem on its asymptotic convergence rate.

第二章首先介绍当系数矩阵是Hermitian正定矩阵时经典交替迭代法的收敛理论和相应的比较理论，同时我们给出了当分裂不同时对迭代渐进收敛率的影响。

In this paper we discuss the optimal approximation of matrices and its numerical algorithm on some closed convex cone .

讨论矩阵在闭凸锥上的最佳逼近及其数值算法，在对称半正定矩阵集上，给出了最佳逼近数值算法的MATLAB程序和数值例子。

Theoretical analysis indicates that the unitary matrix can accurately and simultaneously diagonalize the two matrices.

理论分析表明，该矩阵可以使两个正定矩阵同时精确对角化。

On the other hand, we introduce the convergence theories for generalized alternating method, parallel synchronous iterative methods and parallel alternating synchronous iterative methods when the coefficient matrix are Hermitian positive definite matrices.

接着，讨论了当系数矩阵是Hermitian正定矩阵时广义交替迭代法，并行同步迭代法，并行交替同步迭代法的收敛理论。

Secondly, a conjecture about the stability for these systems is proposed based on the sufficient and necessary condition of the isolated transfer function being positive real. When the zeros and poles of the transfer functions lie in the imaginary axis, a known conclusion is derived from the conjecture; while the zeros and poles are on the real axis, a new result is obtained and is proved in this note. Finally, according to the conjecture, an example with poles existing on the complex plane is presented, which is not only interesting but also challenging.

然后， 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想，当传递函数的零极点都位于虚轴上时，由这一猜想得到了一个已知的结论；当传递函数的零极点都位于实轴上时，由这一猜想得到了一个新的结论，本文证明该结论是正确的；最后，根据这一猜想，给出了传递函数极点位于复平面的一个例子，它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题，值得去深入研究。

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems.

本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形，给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。

Some sufficient and necessary conditions of the full symmetric real matrix is full definite matrix are discussed.

讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。

Positive definite matrix occupies a very important position in matrix theory, and has great value in practice.

正定矩阵在矩阵论中占有十分重要的地位，在实际中也有广泛的应用价值。

Positive definite matrix ; \ inverse matrix ; \ Schur complement of matrix

正定矩阵；逆矩阵；矩阵的Schur补

Based on the relationship between matrix and symmetric matrix global exponential stability of the discrete-time neural networks model and the result of exponential convergence rate were obtained by using the characteristics of eigenvalues of a positive definite matrix and introducing a proper factor.

针对带有边界约束的凸二次规划问题，利用离散神经网络模型的建模原理，构造了一个神经网络模型。利用矩阵与对称矩阵的关系和正定矩阵特征值的性质，通过引入一个适当的因子，得到了该离散型神经网络模型是全局指数稳定性和指数收敛率的结果。同时分析了该结果的优越性和存在的不足，提出了解决的3种方法，最后给出了实例说明本方法取得结果的实用性

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷