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Israel Journal of Mathematics

, Volume 91, Issue 1–3, pp 349–371 | Cite as

The order of a typical matrix with entries in a finite field

  • Eric Schmutz
Article

Abstract

IfA is an invertiblen×n matrix with entries in the finite field Fq, letT n (A) be its minimum period or exponent, i.e. its order as an element of the general linear group GL(n,q). The main result is, roughly, that\(T_n (A) = q^{n - } (log n)^{2 + 0(1)} \) for almost everyA.

Keywords

Finite Field Characteristic Polynomial Moment Generate Function Irreducible Polynomial Typical Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Magnes Press 1995

Authors and Affiliations

  • Eric Schmutz
    • 1
  1. 1.Mathematics and Computer Science DepartmentDrexel UniversityPhiladelphiaUSA

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