同时对角化

As advantage of this method, at the same time of diagonalization, one can know the algebraic structure in the Hamiltonian and get the eigenstates that are revealed to be an algebraic coherent state as well as some other possible information of the corresponding physical system.

这种方法的优点是，在用代数法将哈密顿量对角化的同时，不但得出了该系统哈密顿量的代数形式，并且可以得知对应的本征态与代数相干态的关系及对应的物理系统的其他物理信息。

This paper discusses the matrix of the basic theory of diagonalization. On this basis, it studies the two matrices at the same time or a contract similar to the conditions of diagonalization.

本文论述了矩阵可对角化的基本理论，在此基础上研究了两个矩阵同时相似或合同对角化的条件。

In this paper, the concept of congruent diagonalization of matrix is presented, and the problem of diagonalization of one matrix is generalized.

提出矩阵合同对角化概念，对一个矩阵对角化问题进行推广思考，讨论了二个矩阵的同时对角化问题，取得了一些结果，给出了有关算

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。

Moreover, when the normalized damping matrix is diagonally dominant, it is strictly shown that decoupling the modal equations by neglecting the off-diagonal elements indeed minimizes the error upper bound.

同时，还严格地证明了，当正则化的模态阻尼矩阵是对角占优时，由忽略其非对角线元素使模态方程解耦的方法所引起的误差的上限的确能达到最小。

The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed.

讨论四元数Hermitian矩阵对在共轭合同关系下的同时对角化问题。

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。

Three-way data analysis (Chapter 1 to 5 of Part Ⅰ): In terms of the symmetry of trilinear model, several statistical criteria including coupled vectors resolution errors and slice-wise diagonalization error are proposed for statistically plausible resolution of trilinear data. These criteria form the basis for the development of novel trilinear analysis procedures. In Chapter 1 the coupled vectors resolution method is developed for second-order calibration.

三阶数据分析：利用三线性模型的对称性，提出了耦合向量分辨误差与同时对角化误差等多个三线性分辨的统计准则，这些准则为今后发展三线性分辨方法提供了重要依据。

Constructing a unitary matrix for transformation of coordinates by means of quadratic form theory,the Hamiltonian of the 3D coordinate-momentum coupling harmonic oscillator is transformed into diagonalmatrix,it not only offer a general mathematic method for solving this kind of problems,but also have an active effect upon upgrading students ability to solve physics problems by mathematical theory.

利用二次型理论构造一个幺正矩阵进行表象变换，将|x〉表象中的三模坐标-动量耦合量子谐振子体系的哈密顿量对角化，这不仅提供了一种解决该类问题的一般数学方法，同时对培养和提升学生运用数学工具解决复杂物理问题的能力也具有积极的指导作用。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失