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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 | |