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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 487-491

Equivalence classes of matrices over a finite field

Department of Mathematics, The Pennsylvania State University, Sharon 16146, Pennsylvania, USA

Received 26 October 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let Fq=GF(q) denote the finite field of order q and F(m,q) the ring of m×m matrices over Fq. Let Ω be a group of permutations of Fq. If A,BϵF(m,q) then A is equivalent to B relative to Ω if there exists ϕϵΩ 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.