Max-linear Systems: Theory and Algorithms

This book provides a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general matrices. Among the main features of the proposed book is the presentation of the fundamental max-algebraic theory, in one place in a comprehensive and unified form, made with all proofs and in full generality (that is for both irreducible and reducible matrices). Advanced material within the book also provides the reader with a wealth of information that has never been published before.

Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices.

Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all.

Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.

Provides a reader-friendly introduction for those not familiar with max-algebra, in addition to advanced material for those working in tropical geometry Presents a comprehensive & self-contained theory of max-algebra in full generality Contains results never published before Illustrated with numerical examples; complemented by exercises, & accompanied by both practical &theoretical applications Includes supplementary material: sn.pub/extras

Contenu
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.