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Equivalence classes of matrices over a finite field

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  • Gary L. Mullen

Abstract

Let F q = G F ( q ) denote the finite field of order q and F ( m , q ) the ring of m × m matrices over F q . Let Ω be a group of permutations of F q . If A , B ϵ F ( m , q ) then A is equivalent to B relative to Ω if there exists ϕ ϵ Ω such that ϕ ( A ) = B where ϕ ( A ) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.

Suggested Citation

  • Gary L. Mullen, 1979. "Equivalence classes of matrices over a finite field," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:905426
    DOI: 10.1155/S0161171279000387
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