Equivalence classes of matrices over finite fields

Gary L. Mullen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈Fmn, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(aij) = bij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.

Original languageEnglish (US)
Pages (from-to)61-68
Number of pages8
JournalLinear Algebra and Its Applications
Volume27
Issue numberC
DOIs
StatePublished - Oct 1979

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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