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


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.


Finite Field Characteristic Polynomial Moment Generate Function Irreducible Polynomial Typical Matrix 
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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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