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We work out generalized Schur decomposition of quaternion matrix pencil and give out a sufficient condition for simultaneous unitary diagonalization of two quaternion matrices.

2得到了四元数矩阵束的广义Schur分解及两四元数矩阵可同时酉对角化的一个充分条件。

It is shown that finally this problem turns to the estimation of the real joint eigenvalues of three real matrices and solve the joint eigenvalue estimation by a recently proposed simultaneous diagonalization algorithm.

通过同时对角化算法估计矩阵的联合特征值，获得了参数联合估计的强可辨识性，即允许信号参数在任何一维任意重复，并可以使估计参数实现自动配对。

In this paper,from the view point of engineering realization,the problem of decentralized E-Stabilization of complex giant singular nonlinear systems is cousidered by employing the theory of variable structure contol, the property of diagonal dominant matrices and Lyapunov function.

应用变结构控制理论和对角占优矩阵的性质，结合Lyapunov函数方法，从工程实现的角度考虑并研究了一类复杂巨型广义非线性系统的分散E—镇定问题，在一定条件下。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

This method can find the kernel spaces of different fault distribution matrices through singular value decomposition and use it to remove the influence from residual of specified faults; a fault isolation method is given in the end.

将不同故障分布矩阵进行奇异值分解求取其核空间在分别进行故障影响消除，最后给出了故障诊断分离方法。

Upon the conditions addressed,an improved parameter-dependent l2-l∞ performance criterion is established by the introduction of a slack variable,which exhibits a kind of decoupling between Lyapunov functions and system matrices.

同时应用投影定理，通过引入附加矩阵变量，解除了系统矩阵与依赖于参数的Lyapunov函数矩阵之间的耦合，使所得到的条件更适合于滤波器的综合。

The solution for the non-stationary system is obtained through the stationary disturbed system. The gradients of the system performances to all design variables are derived and they can be used to obtain optimal solution of the systems. More generally, if the performance of the system is a function of the solution of a set of generalized Lyapunov equation, then the gradients of the performance function to the coefficient matrices of the equation can be found in closed form.

文中显示，非静态干扰系统的解可由静态干扰系统求得，而此干扰系统之最佳解，则经由本文所推导的对所有设计变数之系统性能函数梯度获得；一般而言，如果系统之性能函数是一组通式化 Lyapunov 方程式解的函数，则此方程式的系数矩阵之性能函数梯度，可用封闭解表示之。

The condition for the solvability of the controllers is expressed by using the coefficient matrices of the whole system.

控制器的可解性条件由系统的系数矩阵表达，因此不需要矩阵分解，可避免由矩阵分解产生的数值问题。

An inductive learning method for classification based on information theory is proposed, which is a maximum contribution classification method according to the theory of channel transmission in information theory, the definition contribution is developed based on probability distribution of classified space, probability transfer matrices of classified space and feature space and mutual information, then entities is classified by the maximum contribution method.

提出了一种基于信息论的归纳分类学习算法－最大贡献分类算法。该算法根据信息论中信道传输的理论，把类别空间和各特征空间的概率转移矩阵以及互信息结合起来，定义了贡献的概念，从而得出了对给定的观测值，用它的最大贡献作为对实体进行分类的规则。

Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

Green function defined inphase space differs from one in coordinate space by its struc-ture which exhibits nonlocatity in coordinates and oscillatorybehavior with respect to momenta.

在相空间中定义的Green函数不同于通常坐标空间的Green函数，在结构上显示出对坐标的高度非局域性，而对动量则显示出振荡行为。

The upper front part of a saddle;a saddlebow.

前鞍桥马鞍前面的上部分；前鞍桥