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*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*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,*后在抽象地讨论概念时,它们就变得容易理解多了。
这是一本介绍性的线性代数教材,内容翔实,层次清晰,适合作为高等院校理工科数学课的教学用书,还可作为公司职员及工程学研究人员的参考书。

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 Exercise
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 Exercise
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 Exercise
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 Exercise
CHAPTER 5 Eigenvalues and Eigenvectors
INTRODUCTORY EXAMPLE:Dynamical Systems
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 Exercise
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 Exercise
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 Exercise
Appendixes
A Uniqueness of the Reduced Echelon Form
B Complex Numbers
Glossary
Answers to Odd-Numbered Exercises
Index

书评
广大师生对本书前两版的评价很高。第三版在此基础上提供了更多的形象化概念、应用(例如第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Web上增强的技术支持。和以前一样,本书提供了对线性代数和有趣应用的基本介绍。

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**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 Undergraduate Mathematics”在内的几本书。