David C.Lay（美）所著《线性代数及其应用(第3版)(英文版)》在前两版的基础上提供了更多的形象化概念、应用，以及Web上增强的技术支持，本书提供了对线性代数和有趣应用的基本介绍。本书介绍了线性代数最基本的概念、理论和证明，包含大量与实际问题相关的习题，并附有习题答案，提供了丰富的应用以解释工程学、计算机科学、数学、物理学、生物学、经济学和统计学中的基础原理及简单计算。本书是高等院校理工科数学课双语教学用书的不二之选。

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。David C.Lay（美）所著《线性代数及其应用(第3版)(英文版)》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。《线性代数及其应用(第3版)(英文版)》的目的是使学生掌握线性代数最基本的概念、理论和证明。全书首先以常见的方式，具体介绍了线性无关、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。

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双语教学用书，也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 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 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 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