Reference
B. De Schutter and B. De Moor, "A note on the characteristic equation in the
max-plus algebra,"
Linear Algebra and Its Applications,
vol. 261, no. 1-3, pp. 237-250, Aug. 1997.
Abstract
In this paper we discuss the characteristic equation of a matrix in the
max-plus algebra. In their
Linear Algebra and Its
Applications paper (vol. 101, pp. 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 max-plus algebra. We show
that the derivation of Olsder and Roos is not entirely correct and we give the
correct formulas for the coefficients of this alternative version of the
max-algebraic characteristic equation. We also give a counterexample for a
conjecture of Olsder in which he states necessary and sufficient conditions for
the coefficients of the max-algebraic characteristic equation.
Publisher page
Downloads
BibTeX
@article{DeSDeM:96-30,
author = {De Schutter, Bart and De Moor, Bart},
title = {A Note on the Characteristic Equation in the Max-Plus Algebra},
journal = {Linear Algebra and Its Applications},
volume = {261},
number = {1--3},
pages = {237--250},
month = aug,
year = {1997}
}