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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Schmutz, Eric 2008. Splitting fields for characteristic polynomials of matrices with entries in a finite field. Finite Fields and Their Applications, Vol. 14, Issue. 1, p. 250.

    Hansen, Jennie C. and Jaworski, Jerzy 2007. A cutting process for random mappings. Random Structures and Algorithms, Vol. 30, Issue. 1-2, p. 287.

    Evans, Steven N. 2002. Elementary divisors and determinants of random matrices over a local field. Stochastic Processes and their Applications, Vol. 102, Issue. 1, p. 89.

    Schmutz, Eric 1995. The order of a typical matrix with entries in a finite field. Israel Journal of Mathematics, Vol. 91, Issue. 1-3, p. 349.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 114, Issue 3
  • November 1993, pp. 507-515

How random is the characteristic polynomial of a random matrix ?

  • Jennie C. Hansen (a1) and Eric Schmutz (a2)
  • DOI:
  • Published online: 24 October 2008

Every monic, degree n polynomial in Fq[x;] is the characteristic polynomial of at least one n × n matrix (with entries in the finite field Fq), but they do not appear with equal frequency. There is no a priori reason that the characteristic polynomial of a typical matrix should resemble a typical monic degree n polynomial. Nevertheless, we prove a precise version of the following heuristic statement: ‘Excepting its small factors, the characteristic polynomial of a random matrix is random.’

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[7]J. P. S. Kung . The cycle structure of a linear transformation over a finite field. Linear Algebra and its Applications 36 (1981), 141155.

[13]R. Stong . Some asymptotic results on finite vector spaces. Advances in applied mathematics 9 (1988), 167199.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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