Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 6, 2015 - 16:00 to 17:00

Location:

Kidder 237

Local Speaker:

Abstract:

This is joint work with Rob Costa and Patrick Dynes. We prove that if an n x n matrix defined over the field of p-adic numbers 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 an analogue of the Perron-Frobenius theorem for positive real matrices.