Max linear Systems: Theory and Algorithms

Aims to provide a detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. This book includes the presentation of the fundamental max-algebraic theory, often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. 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. A welcome introduction to the subject of max-plus (tropical) linear algebra, and in particular algorithmic problems, Max-linear Systems: Theory and Algorithms offers a consolidation of both new and existing literature, thus filling a much-needed gap. Providing the fundamentals of max-algebraic theory in a comprehensive and unified form, in addition to more advanced material with an emphasis on feasibility and reachability, this book presents a number of new research results. Topics covered range from max-linear systems and the eigenvalue-eigenvector problem to periodic behavior of matrices, max-linear programs, linear independence, and matrix scaling. This book assumes no prior knowledge of max-algebra and much of the theoryis illustrated with numerical examples, complemented by exercises, and accompanied by both practical and theoretical applications. Open problems are also demonstrated. A fresh and pioneering approach to the topic of Max-linear Systems, this book will hold a wide-ranging readership, and will be useful for: • anyone with basic mathematical knowledge wishing to learn essential max-algebraic ideas and techniques • undergraduate and postgraduate students of mathematics or a related degree • mathematics researchers • mathematicians working in industry, commerce or management