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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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