### Abstract

Let F=GF(q) denote the finite field of order q, and F_{mn} the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈F_{mn}, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(a_{ij}) = b_{ij}. 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 language | English (US) |
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Pages (from-to) | 61-68 |

Number of pages | 8 |

Journal | Linear Algebra and Its Applications |

Volume | 27 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1979 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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*Linear Algebra and Its Applications*, vol. 27, no. C, pp. 61-68. https://doi.org/10.1016/0024-3795(79)90031-4

**Equivalence classes of matrices over finite fields.** / Mullen, Gary Lee.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Equivalence classes of matrices over finite fields

AU - Mullen, Gary Lee

PY - 1979/1/1

Y1 - 1979/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49249144798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49249144798&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(79)90031-4

DO - 10.1016/0024-3795(79)90031-4

M3 - Article

AN - SCOPUS:49249144798

VL - 27

SP - 61

EP - 68

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -