What is included with this book?
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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