| Introduction | p. 1 |
| Notation, Definitions and Basic Properties | p. 1 |
| Examples | p. 7 |
| Feasibility and Reachability | p. 9 |
| Multi-machine Interactive Production Process: A Managerial Application | p. 9 |
| MMIPP: Synchronization and Optimization | p. 10 |
| Steady Regime and Its Reachability | p. 11 |
| About the Ground Set | p. 12 |
| Digraphs and Matrices | p. 13 |
| The Key Players | p. 16 |
| Maximum Cycle Mean | p. 17 |
| Transitive Closures | p. 21 |
| Dual Operators and Conjugation | p. 29 |
| The Assignment Problem and Its Variants | p. 30 |
| Exercises | p. 36 |
| Max-algebra: Two Special Features | p. 41 |
| Bounded Mixed-integer Solution to Dual Inequalities: A Mathematical Application | p. 41 |
| Problem Formulation | p. 41 |
| All Solutions to SDI and All Bounded Solutions | p. 42 |
| Solving BMISDI | p. 43 |
| Solving BMISDI for Integer Matrices | p. 45 |
| Max-algebra and Combinatorial Optimization | p. 48 |
| Shortest/Longest Distances: Two Connections | p. 48 |
| Maximum Cycle Mean | p. 49 |
| The Job Rotation Problem | p. 49 |
| Other Problems | p. 51 |
| Exercises | p. 52 |
| One-sided Max-linear Systems and Max-algebraic Subspaces | p. 53 |
| The Combinatorial Method | p. 53 |
| The Algebraic Method | p. 57 |
| Subspaces, Generators, Extremals and Bases | p. 59 |
| Column Space | p. 64 |
| Unsolvable Systems | p. 67 |
| Exercises | p. 69 |
| Eigenvalues and Eigenvectors | p. 71 |
| The Eigenproblem: Basic Properties | p. 71 |
| Maximum Cycle Mean is the Principal Eigenvalue | p. 74 |
| Principal Eigenspace | p. 76 |
| Finile Eigenvectors | p. 82 |
| Finding All Eigenvalues | p. 86 |
| Finding All Eigenvectors | p. 95 |
| Commuting Matrices Have a Common Eigenvector | p. 97 |
| Exercises | p. 98 |
| Maxpolynnmials. The Characteristic Maxpolynomial | p. 103 |
| Maxpolynomials and Their Factorization | p. 105 |
| Maxpolynomiai Equations | p. 111 |
| Characteristic Maxpolynomial | p. 112 |
| Definition and Basic Properties | p. 112 |
| The Greatest Corner Is the Principal Eigenvalue | p. 114 |
| Finding All Essential Terms of a Characteristic Maxpolynomial | p. 116 |
| Special Matrices | p. 123 |
| Cayley-Hamilton in Max-algebra | p. 124 |
| Exercises | p. 126 |
| Linear Independence and Rank. The Simple Image Set | p. 127 |
| Strong Linear Independence | p. 127 |
| Strong Regularity of Matrices | p. 130 |
| A Criterion of Strong Regularit | p. 130 |
| The Simple Image Set | p. 135 |
| Strong Regularity in Linearly Ordered Groups | p. 137 |
| Matrices Similar to Strictly Normal Matrices | p. 138 |
| Gondran-Minoux Independence and Regularity | p. 138 |
| An Application to Discrete-event Dynamic Systems | p. 144 |
| Conclusions | p. 146 |
| Exercises | p. 146 |
| Two-sided Max-linear Systems | p. 149 |
| Basic Properties | p. 150 |
| Easily Solvable Special Cases | p. 151 |
| A Classical One | p. 151 |
| Idempotent Matrices | p. 152 |
| Commuting Matrices | p. 153 |
| Essentially One-sided Systems | p. 153 |
| Systems with Separated Variables-The Alternating Method | p. 156 |
| General Two-sided Systems | p. 162 |
| The Square Case: An Application of Symmetrized Semirings | p. 164 |
| Solution Set is Finitely Generated | p. 169 |
| Exercises | p. 176 |
| Reachability of Eigenspaces | p. 179 |
| Visualization of Spectral Properties by Matrix Scaling | p. 181 |
| Principal Eigenspaces of Matrix Powers | p. 186 |
| Periodic Behavior of Matrices | p. 188 |
| Spectral Projector and the Cyclicity Theorem | p. 188 |
| Cyclic Classes and Ultimate Behavior of Matrix Powers | p. 193 |
| Solving Reachability | p. 196 |
| Describing Attraction Spaces | p. 202 |
| The Core Matrix | p. 203 |
| Circulant Properties | p. 204 |
| Max-linear Systems Describing Attraction Spaces | p. 206 |
| Robustness of Matrices | p. 212 |
| Introduction | p. 212 |
| Robust Irreducible Matrices | p. 213 |
| Robust Reducible Matrices | p. 215 |
| M-robustness | p. 220 |
| Exercises | p. 223 |
| Generalized Eigenproblem | p. 227 |
| Basic Properties of the Generalized Eigenproblem | p. 228 |
| Easily Solvable Special Cases | p. 230 |
| Essentially the Eigenproblem | p. 230 |
| When A and B Have a Common Eigenvector | p. 230 |
| When One of A, B Is a Right-multiple of the Other | p. 231 |
| Narrowing the Search for Generalized Eigenvalues | p. 233 |
| Regularization | p. 233 |
| A Necessary Condition for Generalized Eigenvalues | p. 234 |
| Finding maper C() | p. 235 |
| Narrowing the Search | p. 236 |
| Examples | p. 238 |
| Exercises | p. 241 |
| Max-linear Programs | p. 243 |
| Programs with One-sided Constraints | p. 243 |
| Programs with Two-sided Constraints | p. 245 |
| Problem Formulation and Basic Properties | p. 245 |
| Bounds and Attainment of Optimal Values | p. 247 |
| The Algorithms | p. 251 |
| The Integer Case | p. 253 |
| An Example | p. 255 |
| Exercises | p. 257 |
| Conclusions and Open Problems | p. 259 |
| References | p. 261 |
| Index | p. 269 |
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