Contents__eol__目 录__eol__Preface 8__eol__前言__eol__A Note to Students 15__eol__学生须知__eol__ __eol__Chapter 1 Linear Equations in Linear Algebra 17__eol__第1章 线性代数中的线性方程__eol__INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 17__eol__介绍性示例：经济学与工程领域的线性模型__eol__1.1 Systems of Linear Equations 18__eol__线性方程组__eol__1.2 Row Reduction and Echelon Forms 28__eol__行简化与阶梯形__eol__1.3 Vector Equations 40__eol__向量方程__eol__1.4 The Matrix Equation Ax = b 51__eol__矩阵方程Ax = b__eol__1.5 Solution Sets of Linear Systems 59__eol__线性系统的解集__eol__1.6 Applications of Linear Systems 66__eol__线性系统的应用__eol__1.7 Linear Independence 72__eol__线性无关__eol__1.8 Introduction to Linear Transformations 79__eol__线性变换简介__eol__1.9 The Matrix of a Linear Transformation 87__eol__线性变换的矩阵表示法__eol__1.10 Linear Models in Business, Science, and Engineering 97__eol__商业、科学与工程领域的线性模型__eol__Supplementary Exercises 105__eol__补充习题__eol__Chapter 2 Matrix Algebra 109__eol__第2章 矩阵代数__eol__INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 109__eol__介绍性示例：飞行器设计领域的计算机模型__eol__2.1 Matrix Operations 110__eol__矩阵运算__eol__2.2 The Inverse of a Matrix 120__eol__逆矩阵__eol__2.3 Characterizations of Invertible Matrices 129__eol__可逆矩阵的特征__eol__2.4 Partitioned Matrices 135__eol__分块矩阵__eol__2.5 Matrix Factorizations 141__eol__矩阵分解__eol__2.6 The Leontief Input–Output Model 150__eol__Leontief投入产出模型__eol__2.7 Applications to Computer Graphics 156__eol__矩阵在计算机图形学中的应用__eol__2.8 Subspaces of 164__eol__ 的子空间__eol__2.9 Dimension and Rank 171__eol__维数与秩__eol__Supplementary Exercises 178__eol__补充习题__eol__Chapter 3 Determinants 181__eol__第3章 行列式__eol__INTRODUCTORY EXAMPLE: Random Paths and Distortion 181__eol__介绍性示例：随机路径与失真__eol__3.1 Introduction to Determinants 182__eol__行列式简介__eol__3.2 Properties of Determinants 187__eol__行列式的性质__eol__3.3 Cramer’s Rule, Volume, and Linear Transformations 195__eol__克莱姆法则、体积和线性变换__eol__Supplementary Exercises 204__eol__补充习题 __eol__Chapter 4 Vector Spaces 207__eol__第4章 向量空间__eol__INTRODUCTORY EXAMPLE: Space Flight and Control Systems 207__eol__介绍性示例：航天与控制系统__eol__4.1 Vector Spaces and Subspaces 208__eol__向量空间与子空间__eol__4.2 Null Spaces, Column Spaces, and Linear Transformations 216__eol__零空间、列空间与线性变换__eol__4.3 Linearly Independent Sets; Bases 226__eol__线性无关集合；基__eol__4.4 Coordinate Systems 234__eol__坐标系__eol__4.5 The Dimension of a Vector Space 243__eol__向量空间的维数__eol__4.6 Rank 248__eol__秩__eol__4.7 Change of Basis 257__eol__基变换__eol__4.8 Applications to Difference Equations 262__eol__向量空间在差分方程中的应用__eol__4.9 Applications to Markov Chains 271__eol__向量空间在马尔可夫链中的应用__eol__Supplementary Exercises 280__eol__补充习题__eol__Chapter 5 Eigenvalues and Eigenvectors 283__eol__第5章 特征值与特征向量__eol__INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls 283__eol__介绍性示例：动力系统与花斑猫头鹰__eol__5.1 Eigenvectors and Eigenvalues 284__eol__特征向量与特征值__eol__5.2 The Characteristic Equation 292__eol__特征方程__eol__5.3 Diagonalization 299__eol__对角化__eol__5.4 Eigenvectors and Linear Transformations 306__eol__特征向量与线性变换__eol__5.5 Complex Eigenvalues 313__eol__复特征值__eol__5.6 Discrete Dynamical Systems 319__eol__离散动力系统__eol__5.7 Applications to Differential Equations 329__eol__特征值与特征向量在微分方程中的应用__eol__5.8 Iterative Estimates for Eigenvalues 337__eol__特征值的迭代估计__eol__Supplementary Exercises 344__eol__补充习题__eol__Chapter 6 Orthogonality and Least Squares 347__eol__第6章 正交性与最小二乘__eol__INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation 347__eol__介绍性示例：北美基准面和GPS导航__eol__6.1 Inner Product, Length, and Orthogonality 348内积、长度与正交性__eol__6.2 Orthogonal Sets 356__eol__正交集__eol__6.3 Orthogonal Projections 365__eol__正交投影__eol__6.4 The Gram–Schmidt Process 372__eol__格拉姆-施密特过程__eol__6.5 Least-Squares Problems 378__eol__最小二乘问题__eol__6.6 Applications to Linear Models 386__eol__正交性与最小二乘在线性模型中的应用__eol__6.7 Inner Product Spaces 394__eol__内积空间__eol__6.8 Applications of Inner Product