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线性代数及其应用(第3版)(英文版) [平装] |  |
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线性代数及其应用(第3版)(英文版) [平装] | |
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《线性代数及其应用(第3版)(英文版)》：广大师生对《线性代数及其应用(第3版)(英文版)》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，《线性代数及其应用(第3版)(英文版)》提供了对线性代数和有趣应用的基本介绍。
《线性代数及其应用(第3版)(英文版)》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。
提出了矩阵一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。
作者：（美国）莱（David C.Lay）
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 Undergraduate Mathematics在内的几本书。
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
The response of students and teachers to the first two editions of Linear Algebra and Its 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 modem 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.
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