A $p$-adic Perron–Frobenius theorem
Acta Arithmetica, Tome 174 (2016) no. 2, pp. 175-188
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that if an $n\times n$ matrix defined over ${\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ${\mathbb Q}_p$, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a $p$-adic analogue of the Perron–Frobenius theorem for positive real matrices.
Keywords:
prove times matrix defined mathbb generally arbitrary complete discretely valued non archimedean field satisfies certain congruence property has strictly maximal eigenvalue nbsp mathbb iteration normalized matrix converges projection operator corresponding eigenspace result may viewed p adic analogue perron frobenius theorem positive real matrices
Affiliations des auteurs :
Robert Costa 1 ; Patrick Dynes 2 ; Clayton Petsche 3
@article{10_4064_aa8285_4_2016,
author = {Robert Costa and Patrick Dynes and Clayton Petsche},
title = {A $p$-adic {Perron{\textendash}Frobenius} theorem},
journal = {Acta Arithmetica},
pages = {175--188},
publisher = {mathdoc},
volume = {174},
number = {2},
year = {2016},
doi = {10.4064/aa8285-4-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8285-4-2016/}
}
TY - JOUR AU - Robert Costa AU - Patrick Dynes AU - Clayton Petsche TI - A $p$-adic Perron–Frobenius theorem JO - Acta Arithmetica PY - 2016 SP - 175 EP - 188 VL - 174 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8285-4-2016/ DO - 10.4064/aa8285-4-2016 LA - en ID - 10_4064_aa8285_4_2016 ER -
Robert Costa; Patrick Dynes; Clayton Petsche. A $p$-adic Perron–Frobenius theorem. Acta Arithmetica, Tome 174 (2016) no. 2, pp. 175-188. doi: 10.4064/aa8285-4-2016
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