- 作 者：Sixth Edition
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- 出版年份：2004
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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