A p-adic Perron-Frobenius theorem

• Autorzy: Robert Costa , Patrick Dynes , Clayton Petsche
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 15B51: Stochastic matrices
• 11S99: None of the above, but in this section
• 37P20: Non-Archimedean local ground fields
• 15B48: Positive matrices and their generalizations; cones of matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 174
• Numer: 2
• Strony: 175-188

Daty

wydano

2016

Twórcy

autor

Robert Costa

• Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, MA 02155, U.S.A.

autor

Patrick Dynes

• Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Clemson, SC 29634, U.S.A.

autor

Clayton Petsche

• Department of Mathematics, Oregon State University, Corvallis, OR 97331, U.S.A.

Identyfikatory

DOI

10.4064/aa8285-4-2016