**Reference:**

B. De Schutter,
"Upper bounds for the index of cyclicity of a matrix," Tech. rep.
98-32, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 16 pp., July 1999.
Revised version.

**Abstract:**

We derive upper bounds for the index of cyclicity of a matrix as a
function of the size of the matrix. This result can be used in the
characterization of the ultimate behavior of the sequence of
consecutive powers of a matrix in the max-plus algebra, which has
maximum and addition as its basic operations. If the matrix is
irreducible then it is well known that the ultimate behavior is
cyclic. For reducible matrices the behavior is more complex, but it is
also cyclic in nature. The length of the cycles corresponds to the
index of cyclicity of the given matrix.

Technical report: pdf file (225 KB)

@techreport{DeS:98-32,

author={B. {De Schutter}},

title={{Upper} bounds for the index of cyclicity of a matrix},

number={98-32},

institution={ESAT-SISTA, K.U.Leuven},

address={Leuven, Belgium},

month=jul,

year={1999},

note={Revised version}

}

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