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| Preface | |
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| About the Authors | |
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| Acknowledgments | |
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| Matrices | |
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| Basic Concepts | |
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| Problems 1.1 | |
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| Operations | |
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| Problems 1.2 | |
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| Matrix Multiplication | |
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| Problems 1.3 | |
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| Special Matrices | |
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| Problems 1.4 | |
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| Submatrices and Partitioning | |
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| Problems 1.5 | |
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| Vectors | |
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| Problems 1.6 | |
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| The Geometry of Vectors | |
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| Problems 1.7 | |
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| Simultaneous Linear Equations | |
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| Linear Systems | |
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| Problems 2.1 | |
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| Solutions by Substitution | |
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| Problems 2.2 | |
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| Gaussian Elimination | |
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| Problems 2.3 | |
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| Pivoting Strategies | |
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| Problems 2.4 | |
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| Linear Independence | |
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| Problems 2.5 | |
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| Rank | |
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| Problems 2.6 | |
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| Theory of Solutions | |
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| Problems 2.7 | |
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| Final Comments on Chapter 2 | |
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| The Inverse | |
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| Introduction | |
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| Problems 3.1 | |
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| Calculating Inverses | |
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| Problems 3.2 | |
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| Simultaneous Equations | |
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| Problems 3.3 | |
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| Properties of the Inverse | |
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| Problems 3.4 | |
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| LU Decomposition | |
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| Problems 3.5 | |
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| Final Comments on Chapter 3 | |
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| An Introduction to Optimization | |
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| Graphing Inequalities | |
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| Problems 4.1 | |
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| Modeling with Inequalities | |
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| Problems 4.2 | |
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| Solving Problems Using Linear Programming | |
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| Problems 4.3 | |
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| An Introduction to The Simplex Method | |
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| Problems 4.4 | |
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| Final Comments on Chapter 4 | |
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| Determinants | |
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| Introduction | |
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| Problems 5.1 | |
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| Expansion by Cofactors | |
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| Problems 5.2 | |
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| Properties of Determinants | |
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| Problems 5.3 | |
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| Pivotal Condensation | |
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| Problems 5.4 | |
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| Inversion | |
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| Problems 5.5 | |
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| Cramer's Rule | |
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| Problems 5.6 | |
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| Final Comments on Chapter 5 | |
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| Eigenvalues and Eigenvectors | |
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| Definitions | |
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| Problems 6.1 | |
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| Eigenvalues | |
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| Problems 6.2 | |
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| Eigenvectors | |
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| Problems 6.3 | |
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| Properties of Eigenvalues and Eigenvectors | |
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| Problems 6.4 | |
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| Linearly Independent Eigenvectors | |
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| Problems 6.5 | |
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| Power Methods | |
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| Problems 6.6 | |
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| Matrix Calculus | |
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| Well-Defined Functions | |
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| Prblems 7.1 | |
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| Cayley-Hamilton Theorem | |
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| Problems 7.2 | |
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| Polynomials of Matrices-Distinct Eigenvalues | |
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| Problems 7.3 | |
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| Polynomials of Matrices-General Case | |
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| Problems 7.4 | |
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| Functions of a Matrix | |
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| Problems 7.5 | |
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| The Function e[superscript At] | |
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| Problems 7.6 | |
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| Complex Eigenvalues | |
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| Problems 7.7 | |
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| Properties of e[superscript A] | |
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| Problems 7.8 | |
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| Derivatives of a Matrix | |
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| Problems 7.9 | |
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| Final Comments on Chapter 7 | |
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| Linear Differential Equations | |
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| Fundamental Form | |
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| Problems 8.1 | |
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| Reduction of an nth Order Equation | |
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| Problems 8.2 | |
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| Reduction of a System | |
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| Problems 8.3 | |
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| Solutions of Systems with Constant Coefficients | |
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| Problems 8.4 | |
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| Solutions of Systems-General Case | |
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| Problems 8.5 | |
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| Final Comments on Chapter 8 | |
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| Probability and Markov Chains | |
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| Probability: An Informal Approach | |
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| Problems 9.1 | |
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| Some Laws of Probability | |
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| Problems 9.2 | |
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| Bernoulli Trials and Combinatorics | |
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| Problems 9.3 | |
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| Modeling with Markov Chains: An Introduction | |
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| Problems 9.4 | |
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| Final Comments on Chapter 9 | |
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| Real Inner Products and Least-Square | |
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| Introduction | |
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| Problems 10.1 | |
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| Orthonormal Vectors | |
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| Problems 10.2 | |
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| Projections and QR-Decompositions | |
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| Problems 10.3 | |
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| The QR-Algorithm | |
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| Problems 10.4 | |
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| Least-Squares | |
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| Problems 10.5 | |
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| A Word on Technology | |
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| Answers and Hints to Selected Problems | |
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| Index | |