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Preface to the Second Edition | p. vii |
Preface to the First Edition | p. ix |
Matrix Algebra | |
Matrices | p. 1 |
Operations with Matrices | p. 6 |
Matrices over Rings and Fields | p. 24 |
Systems of Linear Equations | |
Gaussian Elimination | p. 30 |
Elementary Row Operations | p. 41 |
Elementary Matrices | p. 47 |
Determinants | |
Permutations and the Definition of a Determinant | p. 57 |
Basic Properties of Determinants | p. 70 |
Determinants and Inverses of Matrices | p. 78 |
Introduction to Vector Spaces | |
Examples of Vector Spaces | p. 87 |
Vector Spaces and Subspaces | p. 95 |
Linear Independence in Vector Spaces | p. 104 |
Basis and Dimension | |
The Existence of a Basis | p. 112 |
The Row and Column Spaces of a Matrix | p. 126 |
Operations with Subspaces | p. 133 |
Linear Transformations | |
Functions Defined on Sets | p. 152 |
Linear Transformations and Matrices | p. 158 |
Kernel, Image and Isomorphism | p. 178 |
Orthogonality in Vector Spaces | |
Scalar Products in Euclidean Space | p. 193 |
Inner Product Spaces | p. 209 |
Orthonormal Sets and the Grain-Schmidt Process | p. 206 |
The Method of Least Squares | p. 241 |
Eigenvectors and Eigenvalues | |
Basic Theory of Eigenvectors and Eigenvalues | p. 257 |
Applications to Systems of Linear Recurrences | p. 276 |
Applications to Systems of Linear Differential Equations | p. 288 |
More Advanced Topics | |
Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices | p. 303 |
Quadratic Forms | p. 313 |
Bilinear Forms | p. 332 |
Minimum Polynomials and Jordan Normal Form | p. 347 |
Linear Programming | |
Introduction to Linear Programming | p. 370 |
The Geometry of Linear Programming | p. 380 |
Basic Solutions and Extreme Points | p. 391 |
The Simplex Algorithm | p. 399 |
Mathematical Induction | p. 415 |
Answers to the Exercises | p. 418 |
Bibliography | p. 430 |
Index | p. 432 |
Table of Contents provided by Ingram. All Rights Reserved. |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.