**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.

Online version of the paper

Corresponding technical report: pdf file (173 KB)

@article{DeSDeM:96-30,

author={B. {De Schutter} and B. {De Moor}},

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},

doi={10.1016/S0024-3795(96)00407-7}

}

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