| Preface | p. vii |
| Elementary Properties of Nonnegative Matrices | p. 1 |
| Algebraic Properties of Nonnegative Matrices | p. 1 |
| Spectral Properties of Nonnegative Matrices | p. 4 |
| Combinatorial Properties of Nonnegative Matrices | p. 5 |
| M-matrices | p. 10 |
| Notes and Remarks | p. 15 |
| Exercises | p. 16 |
| The Perron-Frobenius Theory for Nonnegative Matrices | p. 19 |
| Perron's Theorem for Positive Matrices | p. 19 |
| Frobenius' Theorem for Irreducible Nonnegative Matrices | p. 26 |
| Ergodic Theorems for Nonnegative Matrices | p. 35 |
| Characterizations of Irreducibility and Primitivity | p. 40 |
| Notes and Remarks | p. 46 |
| Exercises | p. 47 |
| Stochastic Matrices | p. 51 |
| Stochastic Matrices | p. 51 |
| Doubly Stochastic Matrices | p. 57 |
| Inequalities Related to Doubly Stochastic Matrices | p. 65 |
| Ergodic Theorems of Stochastic Matrices | p. 69 |
| Notes and Remarks | p. 71 |
| Exercises | p. 72 |
| Applications of Nonnegative Matrices | p. 75 |
| Finite State Stationary Markov Chains | p. 75 |
| The Web Information Retrieval | p. 81 |
| Discrete Dynamical Geometry | p. 85 |
| Iterative Solutions of Linear Algebraic Equations | p. 90 |
| Notes and Remarks | p. 93 |
| Exercises | p. 94 |
| Fundamental Theory of Positive Operators | p. 97 |
| Banach Lattices | p. 98 |
| Positive Operators | p. 106 |
| Ideals and Projections | p. 114 |
| L-spaces and M-spaces | p. 118 |
| Notes and Remarks | p. 124 |
| Exercises | p. 125 |
| The Spectral Theory of Positive Operators | p. 127 |
| The Spectral Theory of Bounded Linear Operators | p. 127 |
| The Spectral Theory of Positive Operators | p. 137 |
| Ergodic Theorems of Bounded Linear Operators | p. 142 |
| Ergodic Theorems of Positive Operators | p. 146 |
| Notes and Remarks | p. 150 |
| Exercises | p. 152 |
| Markov Operators | p. 155 |
| Definition and Examples of Markov Operators | p. 155 |
| Properties of Markov Operators | p. 161 |
| Ergodic Theorems of Markov Operators | p. 164 |
| Asymptotic Periodicity of Markov Operators | p. 168 |
| Notes and Remarks | p. 177 |
| Exercises | p. 178 |
| Frobenius-Perron Operators | p. 181 |
| Measure-preserving Transformations | p. 181 |
| Frobenius-Perron Operators | p. 184 |
| Existence of Absolutely Continuous Invariant Measures | p. 191 |
| Ergodic Properties of Invariant Measures | p. 199 |
| Notes and Remarks | p. 207 |
| Exercises | p. 208 |
| Composition Operators | p. 211 |
| Positive Functionals on C(K) | p. 211 |
| Invariant Measures of Continuous Transformations | p. 213 |
| Ergodic Theorems of Composition Operators | p. 216 |
| Topological Transitivity and Ergodicity | p. 223 |
| Notes and Remarks | p. 226 |
| Exercises | p. 227 |
| Approximations of Markov Operators | p. 229 |
| Ulam's Piecewise Constant Approximations | p. 230 |
| Piecewise Linear Markov Approximations | p. 237 |
| Convergence Rate of Ulam's Method | p. 246 |
| Convergence Rate of the Markov Method | p. 252 |
| Notes and Remarks | p. 259 |
| Exercises | p. 259 |
| Applications of Positive Operators | p. 261 |
| Positive Approximations of Continuous Functions | p. 261 |
| Evolution Differential Equations | p. 268 |
| Conformational Molecular Dynamics | p. 272 |
| Third Generation Wireless Communications | p. 283 |
| Notes and Remarks | p. 288 |
| Exercises | p. 288 |
| Foundations of Matrix Theory | p. 291 |
| Basic Concepts and Results | p. 291 |
| The Spectral Theory of Matrices | p. 294 |
| Analytic Theory of Matrices | p. 301 |
| Norms and Convergence | p. 304 |
| Basic Operator Theory | p. 307 |
| Banach Spaces | p. 307 |
| Hilbert Spaces | p. 313 |
| Bounded Linear Operators | p. 315 |
| Bounded Linear Functionals and Dual Operators | p. 319 |
| Bibliography | p. 327 |
| Index | p. 333 |
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