查询词典 vector algebra

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier transforms and partial differential equations will also be introduced.

本课程为提供已有常微分方程式基础的同学修习，内容包括线性代数，矩阵运算，特徵值问题，向量的微分与积分，一阶线性微分方程组，傅力叶级数和正交函数，傅力叶转换，并将对椭圆，抛物线，双曲线型式的偏微分方程式作概略介绍。

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier

本课程为提供已有常微分方程式基础的同学修习、内容包括线性代数、矩阵运算、特徵值问题、向量的微分与积分、一阶线性微分方程组、傅力叶级数和正交函数、傅力叶转换、并将对椭圆、抛物线、双曲线型式的偏微分方程式作概略介绍。

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

In this paper, mathematical analysis, linear algebra is more material as the foundation, on the basis of previous studies, will solve a number of the function extreme value methods, such as distribution method, elimination method, the discriminant method, mean inequality method, the geometric method, vector method and derivative method, and so to summarize, and on this basis is given for each method the corresponding examples to illustrate for readers to reference and understanding.

本文以数学分析、线性代数更教材为基础，在前人研究的基础上，将求解函数极值的若干方法，如配方法、消元法、判别式法、均值不等式法、几何法、向量法和导数法等等进行归纳总结，并在此基础上针对每一种方法给出相应的例子加以说明，以便读者参考和理解。

In Chapter 2, we introduce a new scalar function of the vector optimization problem by virtue of the spectral function in Euclidean Jordan algebra. Correspondingly, we define the spectral scalar optimization problem and spectral scalar solution.

第二章借助欧几里德若当代数中谱函数的概念，引入了欧几里德若当代数向量优化新的标量函数——谱标量函数，并进一步定义了相应的谱标量优化问题及其谱标量解。

Pattern recognition ; pattern representation ; geometric algebra ; multi-vector

模式识别；模式表示；几何代数；多向量

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

There is considerable emphasis on linear algebra and vector integral calculus.

本课程是18.014的后续课程，它包括和课程18.02相同的材料，但程度更深，强调严谨的推理和对证明的理解，对线性代数和向量积分也有相当的强调。

Recalling some basic concepts and results on Euclidean Jordan algebra and vector optimization, we outline the contents studied in this thesis.

介绍了本文研究所需的基本概念和相关理论，继而提出了本文所要研究的主要内容。

Meanwhile, the relationship between the trace scalar solution set and the Bo properly K—efficient solution set of the Euclidean Jordan algebra vector optimization problem is es- tablished.

同时，还建立了特殊谱标量解集——迹谱标量解集与Bo恰当K-有效解集的包含关系。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。