David C. Lay：美国奥罗拉大学学士，加州大学洛杉矶分校硕士、博士。自1976年起开始于马里兰大学从事数学的教学与研究工作，阿姆斯特丹大学、自由大学、德国凯撒斯劳滕工业大学访问学者，在函数分析和线性代数领域发表文章30余篇。
目錄：
CHAPTER 1 Linear Equations in Linear Algebra 1
Introductory Example: Linear Models in Economics and Engineering 1
1.1Systems of Linear Equations 2
1.2Row Reduction and Echelon Forms 14
1.3Vector Equations 28
1.4The Matrix Equation Ax = b 40
1.5Solution Sets of Linear Systems 50
1.6Applications of Linear Systems 57
1.7Linear Independence 65
1.8Introduction to Linear Transformations 73
1.9The Matrix of a Linear Transformations 82
1.10Linear Models in Business, Science, and Engineering 92
Supplementary Exercises 102
CHAPTER 2 Matrix Algebra 105
Introductory Example: Computer Models in Aircraft Design 105
2.1Matrix Operations 107
2.2The Inverse of a Matrix 118
2.3Characterizations of Invertible Matrices 128
2.4Partioned Matrices 134
2.5Matrix Factorizations 142
2.6The Leontief Input-Output Modes 152
2.7Applications to Computer Graphics 158
2.8Subspaces of Rn 167
2.9Dimension and Rank 176
Supplementary Exercises 183
CHAPTER 3 Determinants 185
Introductory Example: Determinants in Analytic Geometry 185
3.1Introduction to Determinants 186
3.2Properties of Determinants 192
3.3Cramer’s Rule, Volume, and Linear Transformations 201
Supplementary Exercises 211
CHAPTER 4 Vector Spaces 215
Introductory Example: Space Flight and Control Systems 215
4.1Vector Spaces and Subspaces 216
4.2Null Space, Column Spaces, and Linear Transformations 226
4.3Linearly Independent Sets: Bases 237
4.4Coordinate Systems 246
4.5The Dimension of a Vector Space 256
4.6Rank 262
4.7Change of Basis 271
4.8Applications to Difference Equations 277
4.9Applications to Markov Chains 288
Supplementary Exercises 299
CHAPTER 5 Eigenvalues and Eigenvectors 301
Introductory Example: Dynamical Systems and Spotted Owls 301
5.1Eigenvectors and Eignevalues 302
5.2The Characteristic Equation 310
5.3Diagonalization 319
5.4Eigenvectors and Linear Transformations 327
5.5Complex Eigenvalues 335
5.6Discrete Dynamical Systems 342
5.7Applications to Differential Equations 353
5.8Iterative Estimates for Eigenvalues 363
Supplementary Exercises 370
CHAPTER 6 Orthogonality and Least Squares 373
Introductory Example: Readjusting the North American Datum 373
6.1Inner Product, Length, and Orthogonality 375
6.2Orthogonal Sets 384
6.3Orthogonal Projections 394
6.4The Gram-Schmidt Process 402
6.5Least-Squares Problems 409
6.6Applications to Linear Models 419
6.7Inner Product Spaces 427
6.8Applications of Inner Product Spaces 436
Supplementary Exercises 444
CHAPTER 7 Symmetric Matrices and Quadratic Forms 447
Introductory Example: Multichannel Image Processing 447
7.1Diagonalization of Symmetric Matices 449
7.2Quadratic Forms 455
7.3Constrained Optimization 463
7.4The Singular Value Decomposition 471
7.5Applications to Image Processing and Statistics 482
Supplementary Exercises 444
Appendixes
A Uniqueness of the Reduced Echelon Form A1
B Complex Numbers A3
Glossary A9
Answers to Odd-Numbered Exercises A19
Index I1
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