- 作 者：GILBERT STRANG
- 出 版 社：BROOKS/COLE CENGAGE LEARNING
- 出版年份：2006
- ISBN：0030105676
- 标注页数：488 页
- PDF页数：498 页
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Chapter 1 MATRICES AND GAUSSIAN ELIMINATION 1
1.1 Introduction 1
1.2 The Geometry of Linear Equations 3
1.3 An Example of Gaussian Elimination 11
1.4 Matrix Notation and Matrix Multiplication 19
1.5 Triangular Factors and Row Exchanges 32
1.6 Inverses and Transposes 45
1.7 Special Matrices and Applications 58
Review Exercises: Chapter 1 65
Chapter 2 VECTOR SPACES 69
2.1 Vector Spaces and Subspaces 69
2.2 Solving Ax = 0 and Ax = b 77
2.3 Linear Independence, Basis, and Dimension 92
2.4 The Four Fundamental Subspaces 102
2.5 Graphs and Networks 114
2.6 Linear Transformations 125
Review Exercises: Chapter 2 137
Chapter 3 ORTHOGONALITY 141
3.1 Orthogonal Vectors and Subspaces 141
3.2 Cosines and Projections onto Lines 152
3.3 Projections and Least Squares 160
3.4 Orthogonal Bases and Gram-Schmidt 174
3.5 The Fast Fourier Transform 188
Review Exercises: Chapter 3 198
Chapter 4 DETERMINANTS 201
4.1 Introduction 201
4.2 Properties of the Determinant 203
4.3 Formulas for the Determinant 210
4.4 Applications of Determinants 220
Review Exercises: Chapter 4 230
Chapter 5 EIGENVALUES AND EIGENVECTORS 233
5.1 Introduction 233
5.2 Diagonalization of a Matrix 245
5.3 Difference Equations and Powers Ak 254
5.4 Differential Equations and eAt 266
5.5 Complex Matrices 280
5.6 Similarity Transformations 293
Review Exercises: Chapter 5 307
Chapter 6 POSITIVE DEFINITE MATRICES 311
6.1 Minima, Maxima, and Saddle Points 311
6.2 Tests for Positive Definiteness 318
6.3 Singular Value Decomposition 331
6.4 Minimum Principles 339
6.5 The Finite Element Method 346
Chapter 7 COMPUTATIONS WITH MATRICES 351
7.1 Introduction 351
7.2 Matrix Norm and Condition Number 352
7.3 Computation of Eigenvalues 359
7.4 Iterative Methods for Ax = b 367
Chapter 8 LINEAR PROGRAMMING AND GAME THEORY 377
8.1 Linear Inequalities 377
8.2 The Simplex Method 382
8.3 The Dual Problem 392
8.4 Network Models 401
8.5 Game Theory 408
Appendix A INTERSECTION, SUM, AND PRODUCT OF SPACES 415
Appendix B THE JORDAN FORM 422
Solutions to Selected Exercises 428
Matrix Factorizations 474
Glossary 476
MATLAB Teaching Codes 481
Index 482
Linear Algebra in a Nutshell 488