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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics