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。本书主要包括线性方程组、矩阵代数、行列式、向量空间、特征值和特征向量、正交性和最小二乘方、对称矩阵和二次型等内容。本书的目的是使学生掌握线性代数最基本的概念、理论和证明。首先以常见的方式，具体介绍了线性独立、子空间、向量空间和线性变换等概念，然后逐渐展开，最后在抽象地讨论概念时，它们就变得容易理解多了。
本书是对线性代数及其有趣应用的基本介绍。在前两版的基础上，第三版提供了更多的形象化概念、应用（如1.6节中的列昂捷夫经济学模型、化学方程组和业务流），以及增强的Web支持。
David C. Lay：美国奥罗拉大学学士，加州大学洛杉矶分校硕士、博士，教育家。1976年起开始在马里兰大学从事数学教学与研究工作，阿姆斯特丹大学、自由大学、德国凯撒斯劳滕工业大学访问学者，在函数分析和线性代数领域发表文章30余篇。美国国家科学基金会资助的线性代数课程研究小组的创始人，参与编写了《函数分析、积分及其应用导论》和《线性代数精粹》等书。
CHAPTER 1 Linear Equations in Linear Algebra 1Introductory Example: Linear Models in Economics and Engineering 11.1Systems of Linear Equations 21.2Row Reduction and Echelon Forms 141.3Vector Equations 281.4The Matrix Equation Ax = b 401.5Solution Sets of Linear Systems 501.6Applications of Linear Systems 571.7Linear Independence 651.8Introduction to Linear Transformations 731.9The Matrix of a Linear Transformations 821.10Linear Models in Business, Science, and Engineering 92Supplementary Exercises 102CHAPTER 2 Matrix Algebra 105Introductory Example: Computer Models in Aircraft Design 1052.1Matrix Operations 1072.2The Inverse of a Matrix 1182.3Characterizations of Invertible Matrices 1282.4Partioned Matrices 1342.5Matrix Factorizations 1422.6The Leontief Input-Output Modes 1522.7Applications to Computer Graphics 1582.8Subspaces of Rn 1672.9Dimension and Rank 176Supplementary Exercises 183CHAPTER 3 Determinants 185Introductory Example: Determinants in Analytic Geometry 1853.1Introduction to Determinants 1863.2Properties of Determinants 1923.3Cramer’s Rule, Volume, and Linear Transformations 201Supplementary Exercises 211CHAPTER 4 Vector Spaces 215Introductory Example: Space Flight and Control Systems 2154.1Vector Spaces and Subspaces 2164.2Null Space, Column Spaces, and Linear Transformations 2264.3Linearly Independent Sets: Bases 2374.4Coordinate Systems 2464.5The Dimension of a Vector Space 2564.6Rank 2624.7Change of Basis 2714.8Applications to Difference Equations 2774.9Applications to Markov Chains 288Supplementary Exercises 299CHAPTER 5 Eigenvalues and Eigenvectors 301Introductory Example: Dynamical Systems and Spotted Owls 3015.1Eigenvectors and Eignevalues 3025.2The Characteristic Equation 3105.3Diagonalization 3195.4Eigenvectors and Linear Transformations 3275.5Complex Eigenvalues 3355.6Discrete Dynamical Systems 3425.7Applications to Differential Equations 3535.8Iterative Estimates for Eigenvalues 363Supplementary Exercises 370CHAPTER 6 Orthogonality and Least Squares 373Introductory Example: Readjusting the North American Datum 3736.1Inner Product, Length, and Orthogonality 3756.2Orthogonal Sets 3846.3Orthogonal Projections 3946.4The Gram-Schmidt Process 4026.5Least-Squares Problems 4096.6Applications to Linear Models 4196.7Inner Product Spaces 4276.8Applications of Inner Product Spaces 436Supplementary Exercises 444CHAPTER 7 Symmetric Matrices and Quadratic Forms 447Introductory Example: Multichannel Image Processing 4477.1Diagonalization of Symmetric Matices 4497.2Quadratic Forms 4557.3Constrained Optimization 4637.4The Singular Value Decomposition 4717.5Applications to Image Processing and Statistics 482Supplementary Exercises 444AppendixesA Uniqueness of the Reduced Echelon Form A1B Complex Numbers A3Glossary A9Answers to Odd-Numbered Exercises A19Index I1
新书资讯