线性代数 （英文版·第6版）=Linear Algebra with ApplicationsPDF电子书下载

1 MATRICES AND SYSTEMS OF EQUATIONS 1

1 Systems of Linear Equations 1

2 Row Echelon Form 13

3 Matrix Algebra 33

4 Elementary Matrices 67

5 Partitioned Matrices 79

MATLAB Exercises 91

Chapter Test 97

2 DETERMINANTS 99

1 The Determinant of a Matrix 99

2 Properties of Determinants 107

3 Cramer's Rule 115

MATLAB Exercises 121

Chapter Test 123

3 VECTOR SPACES 125

1 Definition and Examples 125

2 Subspaces 134

3 Linear Independence 144

4 Basis and Dimension 156

5 Change of Basis 163

6 Row Space and Column Space 174

MATLAB Exercises 184

Chapter Test 186

4 LINEAR TRANSFORMATIONS 188

1 Definition and Examples 188

2 Matrix Representations of Linear Transformations 198

3 Similarity 212

MATLAB Exercises 220

Chapter Test 221

5 ORTHOGONALITY 223

1 The Scalar Product in Rn 224

2 Orthogonal Subspaces 239

3 Least Squares Problems 249

4 Inner Product Spaces 260

5 Orthonormal Sets 270

6 The Gram-Schmidt Orthogonalization Process 290

7 Orthogonal Polynomials 299

MATLAB Exercises 307

Chapter Test 310

6 EIGENVALUES 312

1 Eigenvalues and Eigenvectors 313

2 Systems of Linear Differential Equations 326

3 Diagonalization 339

4 Hermitian Matrices 355

5 The Singular Value Decomposition 367

6 Quadratic Forms 382

7 Positive Definite Matrices 397

8 Nonnegative Matrices 405

MATLAB Exercises 412

Chapter Test 421

7 NUMERICAL LINEAR ALGEBRA 422

1 Floating-Point Numbers 423

2 Gaussian Elimination 427

3 Pivoting Strategies 436

4 Matrix Norms and Condition Numbers 442

5 Orthogonal Transformations 458

6 The Eigenvalue Problem 470

7 Least Squares Problems 482

MATLAB Exercises 494

Chapter Test 503

8 ITERATIVE METHODS Web 505

9 JORDAN CANONICAL FORM Web 505

APPENDIX:MATLAB 505

BIBLIOGRAPHY 517

ANSWERS TO SELECTED EXERCISES 520

INDEX 540