David C.Lay，是一位教育家，发表过30余篇关于函数分析和线性代数的研究论文。他还是由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。Lay参与编写了包括Introduction to Functional Analysis 、Calculus and Its Applications和Linear Algebra Gems-Assets for Und
目录
CHAPTER I 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 1.10Linear 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 R 2.9 Dimension and Rank Supplementary Exercises CHAPTER 3Determinants 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 4Vector 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 Lmear 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 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 Appendixes A Uniqueness of the Reduced Echelon Form B Complex Numbers Glossary Answers to Odd-Numbered Exercises Index
