Geodesic
Powers of sign portraits of real matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 5-17 
Yu. A. Alpin; S. N. Il'in. Powers of sign portraits of real matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a0/
@article{ZNSL_2002_284_a0,
     author = {Yu. A. Alpin and S. N. Il'in},
     title = {Powers of sign portraits of real matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     year = {2002},
     volume = {284},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The sign portrait $S$ of a real $n\times n$ matrix is a matrix over the semiring with elements $0,1,-1$ and $\theta$, where $\theta$ symbolizes indeterminateness. It is proved that if $k$ is the least positive integer such that all the entries of $S^k$ are equal to $\theta$ then $k\le2n^2-3n+2$, and this bound is sharp.