In this article, continuing [12,13], further contributions to the theory of max-min convex geometry are given. The max-min semiring is the set R = R βͺ {Β±β} endowed with the operations β = max, β = min in R. A max-min hyperplane (briefly, a hyperplane) is the set of all points x = (x 1 , . . . , x n
The structure of max-plus hyperplanes
β Scribed by V. Nitica; I. Singer
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 420 KB
- Volume
- 426
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
We establish the following max-plus analogue of Minkowski's theorem. Any point of a compact max-plus convex subset of (R βͺ {-β}) n can be written as the max-plus convex combination of at most n + 1 of the extreme points of this subset. We establish related results for closed max-plus cones and close
We investigate the action of semigroups of d Γ d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements. In terms of orbits, our mai
The classical algorithms to align two biological sequences (Needleman and Wunsch and Smith and Waterman algorithms) can be seen as a sequence of elementary operations in (max; +) algebra: each line (viewed as a vector) of the dynamic programming table of the alignment algorithms can be deduced by a
We discuss the characteristic equation of a matrix in the max-plus algebra. In their Linear Algebra Appl. paper [101:87-108 (1988)] Olsder and Roos have used a transformation between the max-plus algebra and linear algebra to show that the Cayley-Hamilton theorem also holds in the maw-plus algebra.
One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results in connection with the minimal realization problem in the max-plus algebra. First we characterize the minimal system order of a max-li