四元数矩阵与域上矩阵的几点差异

比较了四元数矩阵与域上矩阵在左、右特征值、逆矩阵、秩和迹等几个方面的差异,同时给出了四元数矩阵左、右特征值相等的一个充分条件.     

等迹矩阵

对线性代数中的一个古老问题“矩阵A与B有相同特征值的充分必要条件是什么?”给予了完整的回答.先给出了等迹矩阵的定义,然后证明了如下定理:①任意n阶方阵A都等迹于对角矩阵D,且D的对角线元素为A的特征值.②矩阵A与B有相同特征值的充分必要条件是A与B等迹.③相似矩阵必是等迹矩阵,     

实四元数矩阵正则对的广义右特征值

给出了实四元数矩阵正则对的广义右特征值的存在性和表达形式. 通过运用实四元数矩阵的复表示,把实四元数矩阵的问题转化为复矩阵的问题,从而证明了正则对上的实四元数矩阵广义右特征值的存在性和表达形式. 由此有助于研究实四元数矩阵方程的解的情况和解的稳定性.     

四元数矩阵的特征值与特征向量

讨论了四元数矩阵的左、右特征值及特征向量的性质。证明了如下结论：四元数矩阵Ｂ的属于其左特征值λ的所有特征向量添上零向量构成实数域Ｒ上的向量空间；四元数矩阵Ｂ的属于其左特征值λ０的所有特征向量添上零向构成Ｑ上右向量空间Ｑ＾ｎ的子空间，这里Ｑ表示四元数体。     

四元数循环矩阵的特征值

文章给出四元数循环矩阵的左特征值与右特征值的一般表达式,并给出四元数循环矩阵可对角化的一个充要条件。     

四元数体上矩阵的右特征值

讨论实四元数体上方阵的右特征值，并将域上矩阵的一些相应结果推广到实四元数体上。     

四元数体上方阵乘积可交换的充要条件

给出了四元数的矩阵表示及四元数乘积可交换的充要条件,并利用相似矩阵标准形与广义约当分解,讨论了四元数体上方阵乘积可交换的充要条件,并给出了特殊矩阵的乘积可交换阵的形式。     

四元数自共轭矩阵特征值的变分特征及其应用

利用四元数矩阵的复表示及友向量的概念结合复数域上的Hermitian阵的性质证明了四元数自共轭矩阵的特征值的变分特征,并利用变分特征研究了四元数矩阵特征值的性质.得到了四元数矩阵的Wey1定理、单调性定理、柯西分隔定理等一系列结果.     

四元数矩阵的列左秩

建立了四元数矩阵列右秩与列左秩的关系不等式，解决了一类满足列左秩条件的矩阵方程的解存在性问题，给出了一类列左秩与列右秩相等的自共轭四元数矩阵，并针对此类矩阵中的任意两元A和B，构造性地得到了A与B可换的充要条件，进一步就A与B可换情形下，证明了AB的列左秩与列右秩仍相等．最后，就四元数矩阵列左秩的几个相关问题，通过举例作出了回答．     

关于四元数矩阵特征值的两个估计定理

在复数域上,复矩阵的特征值有着许多重要的估计方法,它能很好地表达复矩阵的特征值的分布情况。由于四元数矩阵乘积的非交换性,使得四元数矩阵与复矩阵特征值存在较大差异。利用容易刻画的有界集来估计一个四元数矩阵的特征值,给出了四元数矩阵特征值估计的两个定理。     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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