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AN OVERVIEW OF MAX-PLUS LINEAR SYSTEMS

Kim, Yong-Gu;Shin, Hyun-Hee

  • Received : 2011.02.14
  • Accepted : 2011.02.24
  • Published : 2011.03.25

Abstract

Let $a{\oplus}b$ = max(a, b), $a{\otimes}b$=a+b, a, $b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${\oplus},{\otimes}$) extended to matrices and vectors over $\mathbb{R}_{\varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\mathbb{R}_{\varepsilon}$.

Keywords

Max-plus algebra;Linear equations;Tropical Geometry

References

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  2. P. Butkovic, Max-algebra: the linear algebra of combinatorics? Linear Algebra Appl. bf 367 (2003), 313-335. https://doi.org/10.1016/S0024-3795(02)00655-9
  3. R. Cuninghame-Green, Minimax-Algebra, Lecture Notes in Economics and Math. Systems, Vol. 166, Springer-Verlag, New York, Heidelberg, Berlin 1979.
  4. B. De Schutter, Max-Algebraic system theory for discrete event systems, Katholiceke Universiteit Press, 1994.
  5. D. Speyer, B. Sturmfels, Tropical Matematics, Preprint arXiv:math.Co/04080099.