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 |

Table of Contents provided by Syndetics. All Rights Reserved. |