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Recent years have seen a significant rise of interest in max-linear theory and techniques. In addition to providing the linear-algebraic background in the field of tropical mathematics, max-algebra provides mathematical theory and techniques for solving various nonlinear problems arising in areas such as manufacturing, transportation, allocation of resources and information processing technology. It is, therefore, a significant topic spanning both pure and applied mathematical fields.
Introduction
Max-algebra: Two Special Features
One-sided Max-linear Systems and Max-algebraic Subspaces
Eigenvalues and Eigenvectors
Maxpolynomials. The Characteristic Maxpolynomial
Linear Independence and Rank. The Simple Image Set
Two-sided Max-linear Systems
Reachability of Eigenspaces
Generalized Eigenproblem
Max-linear Programs
Conclusions and Open Problems