Skip to main content
×
Home
    • Aa
    • Aa

How random is the characteristic polynomial of a random matrix ?

  • Jennie C. Hansen (a1) and Eric Schmutz (a2)
Abstract
Abstract

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.’

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 22 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.