Geodesic
A $p$-adic Perron–Frobenius theorem
Robert Costa 1   ; Patrick Dynes 2   ; Clayton Petsche 3
1 Department of Mathematics Tufts University 503 Boston Avenue Medford, MA 02155, U.S.A.
2 Department of Mathematical Sciences Clemson University O-110 Martin Hall Clemson, SC 29634, U.S.A.
3 Department of Mathematics Oregon State University Corvallis, OR 97331, U.S.A.
Acta Arithmetica, Tome 174 (2016) no. 2, pp. 175-188 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa8285-4-2016
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

Robert Costa  1   ; Patrick Dynes  2   ; Clayton Petsche  3

1 Department of Mathematics Tufts University 503 Boston Avenue Medford, MA 02155, U.S.A.
2 Department of Mathematical Sciences Clemson University O-110 Martin Hall Clemson, SC 29634, U.S.A.
3 Department of Mathematics Oregon State University Corvallis, OR 97331, U.S.A. 
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     title = {A $p$-adic {Perron{\textendash}Frobenius} theorem},
     journal = {Acta Arithmetica},
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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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