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LINEAR ALGEBRA AND ITS APPLICATIONS FOURTH EDITION【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

LINEAR ALGEBRA AND ITS APPLICATIONS FOURTH EDITION
  • GILBERT STRANG 著
  • 出版社： BROOKS;COLE CENGAGE LEARNING
  • ISBN：0030105676
  • 出版时间：2006
  • 标注页数：488页
  • 文件大小：80MB
  • 文件页数：498页
  • 主题词：

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图书目录

Chapter 1 MATRICES AND GAUSSIAN ELIMINATION1

1.1 Introduction1

1.2 The Geometry of Linear Equations3

1.3 An Example of Gaussian Elimination11

1.4 Matrix Notation and Matrix Multiplication19

1.5 Triangular Factors and Row Exchanges32

1.6 Inverses and Transposes45

1.7 Special Matrices and Applications58

Review Exercises: Chapter 165

Chapter 2 VECTOR SPACES69

2.1 Vector Spaces and Subspaces69

2.2 Solving Ax = 0 and Ax = b77

2.3 Linear Independence, Basis, and Dimension92

2.4 The Four Fundamental Subspaces102

2.5 Graphs and Networks114

2.6 Linear Transformations125

Review Exercises: Chapter 2137

Chapter 3 ORTHOGONALITY141

3.1 Orthogonal Vectors and Subspaces141

3.2 Cosines and Projections onto Lines152

3.3 Projections and Least Squares160

3.4 Orthogonal Bases and Gram-Schmidt174

3.5 The Fast Fourier Transform188

Review Exercises: Chapter 3198

Chapter 4 DETERMINANTS201

4.1 Introduction201

4.2 Properties of the Determinant203

4.3 Formulas for the Determinant210

4.4 Applications of Determinants220

Review Exercises: Chapter 4230

Chapter 5 EIGENVALUES AND EIGENVECTORS233

5.1 Introduction233

5.2 Diagonalization of a Matrix245

5.3 Difference Equations and Powers Ak254

5.4 Differential Equations and eAt266

5.5 Complex Matrices280

5.6 Similarity Transformations293

Review Exercises: Chapter 5307

Chapter 6 POSITIVE DEFINITE MATRICES311

6.1 Minima, Maxima, and Saddle Points311

6.2 Tests for Positive Definiteness318

6.3 Singular Value Decomposition331

6.4 Minimum Principles339

6.5 The Finite Element Method346

Chapter 7 COMPUTATIONS WITH MATRICES351

7.1 Introduction351

7.2 Matrix Norm and Condition Number352

7.3 Computation of Eigenvalues359

7.4 Iterative Methods for Ax = b367

Chapter 8 LINEAR PROGRAMMING AND GAME THEORY377

8.1 Linear Inequalities377

8.2 The Simplex Method382

8.3 The Dual Problem392

8.4 Network Models401

8.5 Game Theory408

Appendix A INTERSECTION, SUM, AND PRODUCT OF SPACES415

Appendix B THE JORDAN FORM422

Solutions to Selected Exercises428

Matrix Factorizations474

Glossary476

MATLAB Teaching Codes481

Index482

Linear Algebra in a Nutshell488

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