线性代数及其应用 (第3版·英文版) azw3 网盘 高速 下载地址大全 免费

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。

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 Alqebra 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： Determinants in Analytic Geometry 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 Veaor 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 Eiqenvalues and Eiqenvectors 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： Readjusting the North American Datum 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 oflnner 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 Appendixes A Uniqueness of the Reduced Echelon Form B Complex Numbers Glossary Answers to Odd—Numbered Exercises Index

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。

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