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| Preface | p. ix |
| Matrices and Systems of Equations | p. 1 |
| Systems of Linear Equations | p. 1 |
| Row Echelon Form | p. 13 |
| Matrix Algebra | p. 33 |
| Elementary Matrices | p. 67 |
| Partitioned Matrices | p. 79 |
| Matlab Exercises | p. 91 |
| Chapter Test | p. 97 |
| Determinants | p. 99 |
| The Determinant of a Matrix | p. 99 |
| Properties of Determinants | p. 107 |
| Cramer's Rule | p. 115 |
| Matlab Exercises | p. 121 |
| Chapter Test | p. 123 |
| Vector Spaces | p. 125 |
| Definition and Examples | p. 125 |
| Subspaces | p. 134 |
| Linear Independence | p. 144 |
| Basis and Dimension | p. 156 |
| Change of Basis | p. 163 |
| Row Space and Column Space | p. 174 |
| Matlab Exercises | p. 184 |
| Chapter Test | p. 186 |
| Linear Transformations | p. 188 |
| Definition and Examples | p. 188 |
| Matrix Representations of Linear Transformations | p. 198 |
| Similarity | p. 212 |
| Matlab Exercises | p. 220 |
| Chapter Test | p. 221 |
| Orthogonality | p. 223 |
| The Scalar Product in R[superscript n] | p. 224 |
| Orthogonal Subspaces | p. 239 |
| Least Squares Problems | p. 249 |
| Inner Product Spaces | p. 260 |
| Orthonormal Sets | p. 270 |
| The Gram--Schmidt Orthogonalization Process | p. 290 |
| Orthogonal Polynomials | p. 299 |
| Matlab Exercises | p. 307 |
| Chapter Test | p. 310 |
| Eigenvalues | p. 312 |
| Eigenvalues and Eigenvectors | p. 313 |
| Systems of Linear Differential Equations | p. 326 |
| Diagonalization | p. 339 |
| Hermitian Matrices | p. 355 |
| The Singular Value Decomposition | p. 367 |
| Quadratic Forms | p. 382 |
| Positive Definite Matrices | p. 397 |
| Nonnegative Matrices | p. 405 |
| Matlab Exercises | p. 412 |
| Chapter Test | p. 421 |
| Numerical Linear Algebra | p. 422 |
| Floating-Point Numbers | p. 423 |
| Gaussian Elimination | p. 427 |
| Pivoting Strategies | p. 436 |
| Matrix Norms and Condition Numbers | p. 442 |
| Orthogonal Transformations | p. 458 |
| The Eigenvalue Problem | p. 470 |
| Least Squares Problems | p. 482 |
| Matlab Exercises | p. 494 |
| Chapter Test | p. 503 |
| Iterative Methods *Web | |
| Jordan Canonical Form *Web | |
| Matlab | p. 505 |
| Bibliography | p. 517 |
| Answers to Selected Exercises | p. 520 |
| Index | p. 540 |
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