A p-adic Perron-Frobenius theorem

Robert Costa, Patrick Dynes, and Clayton Petsche. "A p-adic Perron-Frobenius theorem." Acta Arithmetica 174.2 (2016): 175-188. <http://eudml.org/doc/286202>.

@article{RobertCosta2016,
abstract = {We prove that if an n×n matrix defined over 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 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.},
author = {Robert Costa, Patrick Dynes, Clayton Petsche},
journal = {Acta Arithmetica},
keywords = {Perron-Frobenius theorem; maximal eigenvalue; $p$-adic and Nonarchimedean fields; iteration of matrices},
language = {eng},
number = {2},
pages = {175-188},
title = {A p-adic Perron-Frobenius theorem},
url = {http://eudml.org/doc/286202},
volume = {174},
year = {2016},
}

TY - JOUR
AU - Robert Costa
AU - Patrick Dynes
AU - Clayton Petsche
TI - A p-adic Perron-Frobenius theorem
JO - Acta Arithmetica
PY - 2016
VL - 174
IS - 2
SP - 175
EP - 188
AB - We prove that if an n×n matrix defined over 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 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.
LA - eng
KW - Perron-Frobenius theorem; maximal eigenvalue; $p$-adic and Nonarchimedean fields; iteration of matrices
UR - http://eudml.org/doc/286202
ER -