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Linear Algebra


作者:
刘金宪 韩骁兵 苏连青 李丽霞
定价:
13.10元
ISBN:
978-7-04-012964-9
版面字数:
220千字
开本:
16开
全书页数:
179页
装帧形式:
平装
重点项目:
暂无
出版时间:
2003-12-15
读者对象:
高等教育
一级分类:
数学与统计学类
二级分类:
理工类专业数学基础课
三级分类:
线性代数(与空间解析几何)

  本书是教育科学“十五”国家规划课题研究成果,对线性代数的内容做了较准确的、深入浅出的英文表述。内容包括行列式、矩阵、向量、方程组解的结构、矩阵的特征值与特征向量等。数学专业技术符号系统与国内现行教学规范一致。分节配备了习题并附有答案。本书适合作为高等院校同名课程双语教学的配套教材,也可以作为英语专业数学课程的教科书,以及数学与应用数学、信息与计算科学专业学科英语的阅读读物。
  • CHAPTER Ⅰ DETERMINANTS
    • §1 Determinants of Order 2 and 3
      • 1.1 Determinants of order 2
      • 1.2 Determinants of order 3
      • 1.3 Exercises
    • §2 Determinants of Ordern
      • 2.1  Defining by numbers of inverted sequence
      • 2.2 Defining by induction
      • 2.3 Exercises
    • §3 Properties of Determinants
      • 3.1 Properties of determinants
      • 3.2 Examples
      • 3.3 Exercises
    • §4 Cramer’ s Rule
      • 4.1 Background
      • 4.2 Cramer’s rule
      • 4.3 Exercises
  • CHAPTER Ⅱ MATRICES
    • §1 Definition of Matrices
      • 1.1 Definition of a matrix
      • 1.2 Determinant of a square matrix
      • 1.3 Transpose of a matrix
      • 1.4 Exercises
    • §2 Addition and Multiplication by a Number
      • 2.1 Addition of matrices
      • 2.2 Multiplication of a matrix by a number
      • 2.3 Calculation rules
      • 2.4 Exercises
    • §3 Multiplication of Matrices
      • 3.1 Definition of multiplication
      • 3.2 Calculation rules
      • 3.3 Unit matrix
      • 3.4 Powers of square matrices
      • 3.5 Exercises
    • §4 Inverse of a Matrix
      • 4.1 Inverse of a matrix of order 2
      • 4.2 Inverse of ann×nmatrix
      • 4.3 Properties of inverse matrices
      • 4.4 Exercises
    • §5 Elementary Operations of a Matrix
      • 5.1 Definition of elementary operations
      • 5.2 Standard form of a matrix
      • 5.3 Elementary square matrix
      • 5.4 Find inverse matrices by elementary operations
      • 5.5 Exercises
    • §6 Rank of a Matrix
      • 6.1 Subdeterminants of a matrix
      • 6.2 Definition of rank of a matrix
      • 6.3 Rank and elementary operations
      • 6.4 Examples
      • 6.5 Exercises
    • §7 Elementary Operations and Elimination
      • 7.1 Representation of equations by matrices
      • 7.2 Elimination in simple cases
      • 7.3 The general case of elimination
      • 7.4 Systems of homogeneous linear equations
      • 7.5 Exercises
  • CHAPTER Ⅲ VECTORS
    • §1 n-dimensional Vectors
      • 1.1 Definition ofn-dimensional vectors
      • 1.2 Linear operations of vectors
      • 1.3 Vector space
      • 1.4 Exercises
    • §2 Linear Relation among Vectors
      • 2.1 Linear combination
      • 2.2 Linear dependence
      • 2.3 Determining the linear dependence
      • 2.4 Exercises
    • §3 Some Theorems about Linear Dependence
    • §4 Rank of a Vector Set
      • 4.1 Subsets of vectors
      • 4.2 Definition of the rank
      • 4.3 Matrix and rank of a vector set
      • 4.4 Exercises
  • CHAPTER Ⅳ STRUCTURE OF SOLUTIONS FOR EQUATIONS
    • §1 Homogeneous Equations
      • 1.1 Properties of solutions
      • 1.2 Systems of fundamental solutions
      • 1.3 General solution
      • 1.4 Exercises
    • §2 Nonhomogeneous Equations
      • 2.1 Structure of solutions
      • 2.2 Examples
      • 2.3 Exercises
  • CHAPTER Ⅴ EIGENVALUES
    • §1 Similar Matrices
      • 1.1 Definition of similarity
      • 1.2 Properties of similar matrices
      • 1.3 Exercises
    • §2 Eigenvalues and Eigenvectors
      • 2.1 Definition of eigenvalues and eigenvectors
      • 2.2 Finding eigenvalues and eigenvectors
      • 2.3 Eigenvalues of similar matrices
      • 2.4 Exercises
    • §3  Conditions of Translating into a Diagonal Form
      • 3.1 In the form of eigenvectors
      • 3.2 In the form of eigenvalues
      • 3.3 Exercises
    • §4  Eigenvalues and Eigenvectors of a Symmetric Matrix
      • 4.1 Scalar product of two vectors
      • 4.2 Orthogonal vector set
      • 4.3 Orthogonal matrix
      • 4.4 Eigenvalues and eigenvectors of a real symmetric matrix
      • 4.5 Exercises
  • ANSWERS TO EXERCISES
  • INDEX
  • REFERENCES

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