线性代数 英文版 第8版PDF电子书下载

1 Matrices and Systems of Equations 1

1.1 Systems of Linear Equations 1

1.2 Row Echelon Form 11

1.3 Matrix Arithmetic 27

1.4 Matrix Algebra 44

1.5 Elementary Matrices 58

1.6 Partitioned Matrices 68

MATLAB？ Exercises 77

Chapter Test A 81

Chapter Test B 82

2 Determinants 84

2.1 The Determinant of a Matrix 84

2.2 Properties of Determinants 91

2.3 Additional Topics and Applications 98

MATLAB Exercises 106

Chapter Test A 108

Chapter Test B 108

3 Vector Spaces 110

3.1 Definition and Examples 110

3.2 Subspaces 117

3.3 Linear Independence 127

3.4 Basis and Dimension 138

3.5 Change of Basis 144

3.6 Row Space and Column Space 154

MATLAB Exercises 162

Chapter Test A 164

Chapter Test B 164

4 Linear Transformations 166

4.1 Definition and Examples 166

4.2 Matrix Representations of Linear Transformations 175

4.3 Similarity 189

MATLAB Exercises 195

Chapter Test A 196

Chapter Test B 197

5 Orthogonality 198

5.1 The Scalar Product in Rn 199

5.2 Orthogonal Subspaces 214

5.3 Least Squares Problems 222

5.4 Inner Product Spaces 232

5.5 Orthonormal Sets 241

5.6 The Gram-Schmidt Orthogonalization Process 259

5.7 Orthogonal Polynomials 269

MATLAB Exercises 277

Chapter Test A 279

Chapter Test B 280

6 Eigenvalues 282

6.1 Eigenvalues and Eigenvectors 283

6.2 Systems of Linear Differential Equations 296

6.3 Diagonalization 307

6.4 Hermitian Matrices 324

6.5 The Singular Value Decomposition 337

6.6 Quadratic Forms 351

6.7 Positive Definite Matrices 364

6.8 Nonnegative Matrices 372

MATLAB Exercises 378

Chapter Test A 384

Chapter Test B 384

7 Numerical Linear Algebra 386

7.1 Floating-Point Numbers 387

7.2 Gaussian Elimination 391

7.3 Pivoting Strategies 398

7.4 Matrix Norms and Condition Numbers 403

7.5 Orthogonal Transformations 417

7.6 The Eigenvalue Problem 428

7.7 Least Squares Problems 437

MATLAB Exercises 448

Chapter Test A 454

Chapter Test B 454

Appendix： MATLAB 456

Bibliography 468

Answers to Selected Exercises 471

Index 485