对角化

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

The completely diagonalized Hamiltonian matrices of 3d2/3d8 ion configuration in the trigonal symmetry have been established by irreducible representation method. Taken into account the influence of the spin-spin coupling interactions omitted in previous publications, the spectra and the constants of crystal structure and zero-field splitting parameters of CsNiCl3 crystal and CsNiCl3: Mg2+ crystal are calculated and the influence of the doping to the spectra, the constants of crystal structure, zero-field splitting parameters and Jahn-Teller effect are studied. The results show that doping can change the structure of crystal which brings about the changes in the spectra and zero-field splitting parameters as well as Jahn-Teller effect.

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵，在考虑了以前工作中被忽略的自旋-自旋耦合作用的基础上计算了CsNiCl3晶体和CsNiCl3：Mg2+晶体的基态能级、晶体结构、零场分裂参量和Jahn-Teller效应，研究了掺入Mg2+对CsNiCl3晶体的光谱、零场分裂参量及Jahn-Teller效应的影响和自旋单重态对基态能级的贡献，发现掺杂使得晶体结构产生畸变，从而改变晶体光谱的精细结构和零场分裂参量，不改变Jahn-Teller效应的分裂规律但改变分裂的大小。

The complete diagonalized Hamiltonian matrixes of order 120 of 3d~3/3d~7 ions configuration in the trigonal symmetry have been established by irreducible representation method and group theory,taking spin-orbit interaction,spin-spin interaction and spin-other-orbit interaction into account.

应用不可约张量方法和群的理论构造了三角对称晶场中考虑自旋-轨道相互作用，自旋-自旋相互作用和自旋-其它轨道相互作用的3d3/3d7态离子的可完全对角化的120阶微扰哈密顿矩阵。

The completely diagonalized Hamiltonian matrices of 3d2／3d8 ion configuration in the trigonal symmetry sites have been established by irreducible representation method. Taken into account microscopic magnetic interactions, the spectral fine structure, local structure and zero-field splitting parameters of V3+:α-Al2O3 and Ni2+:α-Al2O3 crystals are investigated as well as the influence of the doping.

应用不可约张量方法构造了三角晶场中3d2/3d8态离子的45阶可完全对角化的能量哈密顿矩阵，在考虑了微小磁相互作用的基础上计算了V3+：α-Al2O3和Ni2+：α-Al2O3晶体的光谱精细结构、晶体局域结构和零场分裂参量，研究了掺入Ni2+和V3+对α-Al2O3晶体光谱精细结构、晶体局域结构和零场分裂参量的影响。

The completely diagonalized Hamiltonian matrixes of order 120 of 3d3/3d7 ions configuration in the trigonal symmetry have been established by irreducible representation method and group theory,taking into account spin-orbit interaction and spin-spin interaction.The ground-state energy levels,the zero-splitting parameter and Jahn-Teller effect of ruby crystal were calculated with the matrixes.

应用不可约张量方法和群的理论构造了三角对称晶场中考虑自旋-轨道相互作用，自旋-自旋相互作用的3d3/3d7离子的可完全对角化的120阶微扰哈密顿矩阵，利用该矩阵计算了红宝石晶体的基态能级、零场分裂参量和Jahn-Teller效应，研究了自旋-轨道的自旋二重态对基态能级的贡献，证明其二重态对基态能级的贡献是不可忽略的，理论计算值与实验值相符合。

With the assumption that electric field is constant within each element, the relationship of the degrees of freedom over each element is determined by introducing a local affine coordinate system.

在单元内部电场为常量场的假设下，使用局部仿射坐标架，确定出每个单元上自由度所服从的约束关系，由此导出对角化质量矩阵的公式。

In the perturbation approach the ro-vibrational Hamiltonian is expanded in terms of the normal coordinates, their conjugate momenta, and the rotational momenta. The harmonic oscillator and rigid rotor wavefunctions are then used as the basis functions.

根据光谱理论，在谐振子和刚性转子的表象中，通过切变换导出一个等效的哈密顿量，考虑各种共振相互作用后，对角化哈密顿矩阵得到本征能量。

The diagonalization of a normal matrix by a unitary transformation.

这一关系在对角化后仍旧为真。粗鄙下流的举动；粗话；下流话

Introduction of Probability, Schrodinger Equation, Uncertainty Principle, One Dimensional Quantum Systems, Linear Space and Matrices, Diagonalization of Matrices, Eigenvalues and Eigenvectors, Similarity Transformation, Central Field Systems, Helium Atoms, Angular Momentum.

量子力学( S0310)(3，0)机率简介、薛丁格方程式、测不准原理、一维量子系统、线性空间及矩阵、矩阵的对角化、本徵值及本徵向量、相似变换、中心场系统、氢原子系统、角动量。

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。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。