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线性代数及其应用：英文版
作者：（美）David C.Lay著
出版社：电子工业出版社
出版时间：2004-03-01
ISBN：9787505396258
定价：¥49.00
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内容简介
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
作者简介
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。
目录
Chapter 1 Linear Equations in Linear Algebra 1
INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 1
1.1 Systems of Linear Equations 2
1.2 Row Reduction and Echelon Forms 14
1.3 Vector Equations 28
1.4 The Matrix Equation Ax =b 40
1.5 Solution Sets of Linear Systems 50
1.6 Applications of Linear Systems 57
1.7 Linear Independence 65
1.8 Introduction to Linear Transformations 73
1.9 The Matrix of a Linear Transformation 82
1.10 Linear Models in Business, Science, and Engineering 92
Supplementary Exercises. 102
Chapter 2 Matrix Alflebra 105
INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 105
2.1 Matrix Operations 107
2.2 The Inverse of a Matrix 118
2.3 Characterizations of Invertible Matrices 128
2.4 Partitioned Matrices 134
2.5 Matrix Factorizations 142
2.6 The Leontief Input-Output Model 152
2.7 Applications to Computer Graphics 158
2.8 Subspaces of R 167
2.9 Dimension and Rank 176
Supplementary Exercises 183
Chapter 3 Determinants 185
INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry 185
3.1 Introduction to Determinants 186
3.2 Properties of Determinants 192
3.3 Cramer's Rule, Volume, and Linear Transformations 201
Supplementary Exercises 211
Chapter 4 Vector Spaces 215
INTRODUCTORY EXAMPLE: Space Flight and Control Systems 215
4.1 Vector Spaces and Subspaces 216
4.2 Null Spaces, Column Spaces, and Linear Transformations 226
4.3 Linearly Independent Sets; Bases 237
4.4 Coordinate Systems 246
4.5 The Dimension of a Vector Space 256
4.6 Rank 262
4.7 Change of Basis 271
4.8 Applications to Difference Equations 277
4.9 Applications to Markov Chains 288
Supplementary Exercises 299
Chapter 5 Eigenvalues and Eigenvectors 301
INTRODUCTORY EXAMPLE' Dynamical Systems and Spotted Owls 301
5.1 Eigenvectors and Eigenvalues 302
512 The Characteristic Equation 310
5.3 Diagonalization 319
5.4 Eigenvectors and Linear Transformations 327
5.5 Complex Eigenvaiues 335
5.6 Discrete Dynamical Systems 342
5.7 Applications to Differential Equations 353
5.8 terative Estimates for Eigenvalues 363
Supplementary Exercises 370
Chapter 6 Orthogonality and Least Squares 373
INSTRODUCTORY EXAMPLE: Readjusting the North American Datum 373
6.1 Inner Product, Length, and Orthogonality 375
6.2 Orthogonal Sets 384
6.3 Orthogonal Projections 394
6.4 The Gram-Schmidt Process 402
6.5 Least-Squares Problems 409
6.6 Applications to Linear Models 419
6.7 Inner Product Spaces 427
6.8 Applications of Inner Product Spaces 436
Supplementary Exercises 444
Chapter 7 Symmetric Matrices and Quadratic Forms 447
INSTRODUCTORY EXAMPLE: Multichannel Image Processing 447
7.1 Diagonalization of Symmetric Matrices 449
7.2 Quadratic Forms 455
7.3 Constrained Optimization 463
7.4 The Singular Value Decomposition 471
7.5 Applications to Image Processing and Statistics 482
Supplementary Exercises 491
Appendixes
A Uniqueness of the Reduced Echelon Form A1
B Complex Numbers A3
Glossary A9
Answers to Odd-Numbered Exercises A19
Index II
INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 1
1.1 Systems of Linear Equations 2
1.2 Row Reduction and Echelon Forms 14
1.3 Vector Equations 28
1.4 The Matrix Equation Ax =b 40
1.5 Solution Sets of Linear Systems 50
1.6 Applications of Linear Systems 57
1.7 Linear Independence 65
1.8 Introduction to Linear Transformations 73
1.9 The Matrix of a Linear Transformation 82
1.10 Linear Models in Business, Science, and Engineering 92
Supplementary Exercises. 102
Chapter 2 Matrix Alflebra 105
INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 105
2.1 Matrix Operations 107
2.2 The Inverse of a Matrix 118
2.3 Characterizations of Invertible Matrices 128
2.4 Partitioned Matrices 134
2.5 Matrix Factorizations 142
2.6 The Leontief Input-Output Model 152
2.7 Applications to Computer Graphics 158
2.8 Subspaces of R 167
2.9 Dimension and Rank 176
Supplementary Exercises 183
Chapter 3 Determinants 185
INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry 185
3.1 Introduction to Determinants 186
3.2 Properties of Determinants 192
3.3 Cramer's Rule, Volume, and Linear Transformations 201
Supplementary Exercises 211
Chapter 4 Vector Spaces 215
INTRODUCTORY EXAMPLE: Space Flight and Control Systems 215
4.1 Vector Spaces and Subspaces 216
4.2 Null Spaces, Column Spaces, and Linear Transformations 226
4.3 Linearly Independent Sets; Bases 237
4.4 Coordinate Systems 246
4.5 The Dimension of a Vector Space 256
4.6 Rank 262
4.7 Change of Basis 271
4.8 Applications to Difference Equations 277
4.9 Applications to Markov Chains 288
Supplementary Exercises 299
Chapter 5 Eigenvalues and Eigenvectors 301
INTRODUCTORY EXAMPLE' Dynamical Systems and Spotted Owls 301
5.1 Eigenvectors and Eigenvalues 302
512 The Characteristic Equation 310
5.3 Diagonalization 319
5.4 Eigenvectors and Linear Transformations 327
5.5 Complex Eigenvaiues 335
5.6 Discrete Dynamical Systems 342
5.7 Applications to Differential Equations 353
5.8 terative Estimates for Eigenvalues 363
Supplementary Exercises 370
Chapter 6 Orthogonality and Least Squares 373
INSTRODUCTORY EXAMPLE: Readjusting the North American Datum 373
6.1 Inner Product, Length, and Orthogonality 375
6.2 Orthogonal Sets 384
6.3 Orthogonal Projections 394
6.4 The Gram-Schmidt Process 402
6.5 Least-Squares Problems 409
6.6 Applications to Linear Models 419
6.7 Inner Product Spaces 427
6.8 Applications of Inner Product Spaces 436
Supplementary Exercises 444
Chapter 7 Symmetric Matrices and Quadratic Forms 447
INSTRODUCTORY EXAMPLE: Multichannel Image Processing 447
7.1 Diagonalization of Symmetric Matrices 449
7.2 Quadratic Forms 455
7.3 Constrained Optimization 463
7.4 The Singular Value Decomposition 471
7.5 Applications to Image Processing and Statistics 482
Supplementary Exercises 491
Appendixes
A Uniqueness of the Reduced Echelon Form A1
B Complex Numbers A3
Glossary A9
Answers to Odd-Numbered Exercises A19
Index II
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