### 基本信息

- 原书名：Linear Algebra and Its Applications(Third Edition)
- 原出版社： Addison Wesley/Pearson

- 作者：
**[美]David C.Lay** - 丛书名：
**高等学校教材系列** - 出版社：电子工业出版社
- ISBN：
**7505396250** - 上架时间：2004-4-21
- 出版日期：2004 年3月
- 开本：16开
- 页码：560
- 版次：1-1
- 所属分类：数学 > 代数，数论及组合理论 > 线性代数

教材 > 研究生/本科/专科教材 > 理学 > 数学

### 内容简介

数学书籍

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。 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。 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。

本书特点：

·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

·提出了矩阵—向量乘法的动态和图形观点，将向量空间的概念引入线性系统的学习中，介绍了正交性和最小二乘方问题

·强调在科学和工程学领域，计算机对于线性代数发展和实践的影响。注释部分是关于如何区分理论上的概念（如矩阵求逆）与计算机实现（如LU因式分解）的内容

·用小图标标记的部分可以在网站www.laylinalgebra.com（或www.mymathlab.com）上找到相关的技术支持，包含习题的数据文件、实例学习和应用方案等内容

### 作译者

### 目录

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

### 前言

Applications has been most gratifying. This Third Edition offers even more visualization of concepts, along with enhanced technology support on the web for both students and instructors. As before, the text provides a modern elementary introduction to linear algebra and a broad selection of interesting applications. The material is accessible to students with the maturity that should come from successful completion of two semesters of college-level mathematics, usually calculus.

The main goal of the text is to help students master the basic concepts and skills they will use later in their careers. The topics here follow the recommendations of the Linear Algebra Curriculum Study Group, which were based on a careful investigation of the real needs of the students and a consensus among professionals in many disciplines that use linear algebra. Hopefully, this course will be one of the most useful and interesting mathematics classes taken as an undergraduate.

DISTINCTIVE FEATURES

Early Introduction of Key Concepts

Many fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas, visualized through the geometric intuition developed in Chapter 1. A major achievement of the text, I believe, is that the level of difficulty is fairly even throughout the course.

A Modern View of Matrix Multiplication

Good notation is crucial, and the text reflects the way scientists and engineers actually use linear algebra in practice. The definitions and proofs focus on the columns of a matrix rather than on the matrix entries. A central theme is to view a matrix-vector product Ax as a linear combination of the coluums of A. This modem approach simplifies many arguments, and it ties vector space ideas into the study of linear systems.

Linear Transformations

Linear transformations form a "thread" that is woven into the fabric of the text. Their use enhances the geometric flavor of the text. In Chapter 1, for instance, linear transformations provide a dynamic and graphical view of matrix-vector multiplication.

Eigenvalues and Dynamical Systems

Eigenvalues appear fairly early in the text, in Chapters 5 and 7. Because this material is spread over several weeks, students have more time than usual to absorb and review these critical concepts. Eigenvalues are motivated by and applied to discrete and continuous dynamical systems, which appear in Sections 1.10, 4.8, 4.9, and in five sections of Chapter 5. Some courses reach Chapter 5 after about five weeks by covering Sections 2.8 and 2.9 instead of Chapter 4. These two optional sections present all the vector space concepts from Chapter 4 needed for Chapter 5.

Orthogonality and Least-Squares Problems

These topics receive a more comprehensive treatment than is commonly found in beginning texts. The Linear Algebra Curriculum Study Group has emphasized the need for a substantial unit on orthogonality and least-squares problems, because orthogonality plays such an important role in computer calculations and numerical linear algebra and because inconsistent linear systems arise so often in practical work.

PEDAGOGICAL FEATURES

Applications

A broad selection of applications illustrates the power of linear algebra to explain fundamental principles and simplify calculations in engineering, computer science, mathematics, physics, biology, economics, and statistics. Some applications appear in separate sections; others are treated in examples and exercises. In addition, each chapter opens with an introductory vignette that sets the stage for some application of linear algebra and provides a motivation for developing the mathematics that follows. Later, the text returns to that application in a section neat the end of the chapter.

A Strong Geometric Emphasis

Every major concept in the course is given a geometric interpretation, because many students learn better when they can visualize an idea. There are substantially more drawings here than usual, and some of the figures have never appeared before in a linear algebra text.

Examples