- 线性代数及其应用(第5版英文版)/高等学校教材系列
- - 作者：(美)戴维·C.莱//史蒂文·R.莱//朱迪·J.麦克唐纳|责编:谭海平
  - 出版社：电子工业
  - ISBN：9787121396175
  - 出版日期：2020/09/01
  - 页数：565
- 售价：39.6

内容大纲
线性代数是处理矩阵和向量空间的数学分支科学，在现代数学的各个领域都有应用。本书内容主要包括线性代数中的线性方程、矩阵代数、行列式、向量空间、特征值与特征向量、正交性与最小二乘、对称矩阵与二次型、向量空间解析几何等，目的是让学生掌握线性代数的基本概念、理论和证明。全书内容简洁、例题丰富、版式美观，除介绍基本概念外，还介绍了它们在各个领域中的具体应用。
本书是一本介绍性的线性代数教材，内容翔实，层次清晰，适合作为高等学校理工科数学课程的双语教学用书，也可作为公司职员及工程学研究人员的参考书。
作者介绍
目录
Preface
A Note to Students
Chapter 1  Linear Equations in Linear Algebra
  INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering
  1.1  Systems of Linear Equations
  1.2  Row Reduction and Echelon Forms
  1.3  Vector Equations
  1.4  The Matrix Equation Ax=b
  1.5  Solution Sets of Linear Systems
  1.6  Applications of Linear Systems
  1.7  Linear Independence
  1.8  Introduction to Linear Transformations
  1.9  The Matrix of a Linear Transformation
  1.10  Linear Models in Business, Science, and Engineering
  Supplementary Exercises
Chapter 2  Matrix Algebra
  INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design
  2.1  Matrix Operations
  2.2  The Inverse of a Matrix
  2.3  Characterizations of Invertible Matrices
  2.4  Partitioned Matrices
  2.5  Matrix Factorizations
  2.6  The Leontief Input–Output Model
  2.7  Applications to Computer Graphics
  2.8  Subspaces of Rn
  2.9  Dimension and Rank
  Supplementary Exercises
Chapter 3   Determinants
  INTRODUCTORY EXAMPLE: Random Paths and Distortion
  3.1  Introduction to Determinants
  3.2  Properties of Determinants
  3.3  Cramer's Rule, Volume, and Linear Transformations
  Supplementary Exercises
Chapter 4  Vector Spaces
  INTRODUCTORY EXAMPLE: Space Flight and Control Systems
  4.1  Vector Spaces and Subspaces
  4.2  Null Spaces, Column Spaces, and Linear Transformations
  4.3  Linearly Independent Sets; Bases
  4.4  Coordinate Systems
  4.5  The Dimension of a Vector Space
  4.6  Rank
  4.7  Change of Basis
  4.8  Applications to Difference Equations
  4.9  Applications to Markov Chains
  Supplementary Exercises
Chapter 5  Eigenvalues and Eigenvectors
  INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls
  5.1  Eigenvectors and Eigenvalues
  5.2  The Characteristic Equation
  5.3  Diagonalization

  5.4  Eigenvectors and Linear Transformations
  5.5  Complex Eigenvalues
  5.6  Discrete Dynamical Systems
  5.7  Applications to Differential Equations
  5.8  Iterative Estimates for Eigenvalues
  Supplementary Exercises
Chapter 6  Orthogonality and Least Squares
  INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation
  6.1  Inner Product, Length, and Orthogonality
  6.2  Orthogonal Sets
  6.3  Orthogonal Projections
  6.4  The Gram-Schmidt Process
  6.5  Least-Squares Problems
  6.6  Applications to Linear Models
  6.7  Inner Product Spaces
  6.8  Applications of Inner Product Spaces
  Supplementary Exercises
Chapter 7  Symmetric Matrices and Quadratic Forms
  INTRODUCTORY EXAMPLE: Multichannel Image Processing
  7.1  Diagonalization of Symmetric Matrices
  7.2  Quadratic Forms
  7.3  Constrained Optimization
  7.4  The Singular Value Decomposition
  7.5  Applications to Image Processing and Statistics
  Supplementary Exercises
Chapter 8  The Geometry of Vector Spaces
  INTRODUCTORY EXAMPLE: The Platonic Solids
  8.1  Affine Combinations
  8.2  Affine Independence
  8.3  Convex Combinations
  8.4  Hyperplanes
  8.5  Polytopes
  8.6  Curves and Surfaces
Chapter 9  Optimization (Online)
  INTRODUCTORY EXAMPLE: The Berlin Airlift
  9.1  Matrix Games
  9.2  Linear Programming—Geometric Method
  9.3  Linear Programming—Simplex Method
  9.4  Duality
Chapter 10  Finite-State Markov Chains (Online)
  INTRODUCTORY EXAMPLE: Googling Markov Chains
  10.1  Introduction and Examples
  10.2  The Steady-State Vector and Google's PageRank
  10.3  Communication Classes
  10.4  Classification of States and Periodicity
  10.5  The Fundamental Matrix
  10.6  Markov Chains and Baseball Statistics
Appendixes
  A  Uniqueness of the Reduced Echelon Form
  B  Complex Numbers

Glossary
Answers to Odd-Numbered Exercises

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作者介绍

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