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线性代数导引（英文版）（Introduction to Linear Algebra)
  • 书号：9787030188885
    作者：谭炳均
  • 外文书名：Linear Algebra
  • 装帧：平装
    开本：B5
  • 页数：424
    字数：150000
    语种：英文
  • 出版社：科学出版社
    出版时间：2007-05
  • 所属分类：O15 代数、数论、组合理论
  • 定价： ￥58.00元
    售价： ￥45.82元
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目录

  • Foreword (Originally in Chinese)
    Preface (for the English translation edition)
    A Note from the Translator
    Explanation for the Special Notational Device [. . .]
    Chapter 0 Integers, Number Fields and Polynomials
    §1 Sets,Mappings and Operations
    §2 Integers
    §3 Number fields
    §4 Polynomials and Polynomial Functions
    §5 Division with Remainder and Remainder Theorem
    §6 Greatest Common Factors and Least Common Multiples
    §7 Factorization andMultiple Factors
    §8 Polynomials over C, R and Q
    §9 Fermat’s Last Theoremon Polynomials
    Exercises
    Part I General Theory of Systems of Linear Equations Introduction
    Setting-up of Systems of Linear Equations and Method of Elimination
    §1 Setting-up of Systems of Linear Equations
    §2 Method of Elimination and Elementary Operations on AugmentedMatrices
    §3 Some Remarks Exercises
    Chapter 1 Algebra of Matrices
    §1 Algebra ofMatrices
    §2 Elementary Operations on Matrices and Canonical Forms
    §3 Partitioned Matrices
    Exercises
    Chapter 2 The Determinant Method for a Special Class of Linear Equations (Cramer’s Rule)
    §1 Determinants (for Square Matrices) of Order n
    §2 Basic Properties of Determinants and their Applications
    §3 Cramer’s rule for systems of linear equations
    §4 Expansion Formula of Determinants
    §5 Axiomatic Definition of Determinants
    Exercises
    Chapter 3 General Theory of Systems of Linear Equations
    §1 Linear Dependence of Vectors of n-Tuples and Solvability of Systems of Linear Equations
    §2 The Rank of a Matrix and Solvability of a System of Linear Equations
    §3 Structure of Solutions of a Systemof Linear Equations
    Exercises
    Chapter 4 Linear Spaces and Systems of Linear Equations
    §1 Linear Spaces and Their Subspaces
    §2 Dimensions, Bases, Coordinates and Cramer’s Rule
    §3 Change of Coordinates and Cramer’s Rule
    §4 Isomorphisms of Linear Spaces and an Application of the Theory of Systems of Linear Equations
    §5 Geometric Structure of Solution Sets of Systems of Linear Equations
    Exercises
    Chapter 5 Symmetric Bilinear Metric Spaces and Systems of Linear Equations
    §1 Linear and Bilinear Functionals on Linear Spaces
    §2 Symmetric Bilinear Metric Spaces and Geometric Explanation for Solvability of Systems of Linear Equations
    §3 Euclidean Spaces
    §4 Distance from a Vector to a Subspace and the Least Squares Method for Systems of Linear Equations
    Exercises
    Part II The Principal Axes Problem of Real Quadratic Forms Introduction
    Geometric Origin of the Principal Axes Problem of Quadratic Forms
    §1 General Problemof Quadratic Forms
    §2 Quadratic Curves-Geometric Origin of the Principal Axes Problem of Quadratic Forms
    Exercises
    Chapter 6 Linear Transformations on Linear Spaces
    §1 Linear Transformations, Their Compositions and Matrix Representations
    §2 Invariant Subspaces, Eigenvalues and Eigenvectors
    §3 Characteristic Polynomials andMinimal Polynomials
    Exercises
    Chapter 7 A Class of Direct Sum Decompositions of Linear Spaces Relative to Linear Transformations
    §1 The Image and Kernel of a Linear Transformation
    §2 A Class of Direct Sum Decompositions of a Linear Space relative to a Linear Transformation
    Exercises
    Chapter 8 Two Classes of Linear Transformations on Euclidean Spaces and the Principal Axes Problem of Quadratic Forms
    §1 Orthogonal Transformations and Symmetric Transformations
    §2 The Principal Axes Problemof Quadratic Forms
    §3 An Application (Reducing Two Real Quadratic Forms into Sums of Squares Simultaneously)
    §4 The General Problemof Quadratic Forms Exercises
    Chapter 9 Further Development—Similarity Canonical Forms of Matrices
    §1 λ-Matrices and Their Equivalence Canonical Forms
    §2 Determinantal Divisors, Invariant Divisors, and Elementary Divisors of λ-matrices
    §3 Similarity of Matrices and Equivalence of Their Characteristic Matrices
    §4 Invariant Divisors of Matrices and Frobenius (Rational) Canonical Forms
    §5 Elementary Divisors of Matrices and Jacobson (Special Case:Jordan) Canonical Forms
    §6 Geometric Interpretations of Frobenius Canonical Forms and Jacobson Canonical Forms
    Exercises
    Bibliography
    Index
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