International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 583823 | https://doi.org/10.1155/S0161171281000367

Gary L. Mullen, "Permutation matrices and matrix equivalence over a finite field", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 583823, 10 pages, 1981. https://doi.org/10.1155/S0161171281000367

Permutation matrices and matrix equivalence over a finite field

Received21 Mar 1980
Revised12 Aug 1980

Abstract

Let F=GF(q) denote the finite field of order q and Fm×n the ring of m×n matrices over F. Let 𝒫n be the set of all permutation matrices of order n over F so that 𝒫n is ismorphic to Sn. If Ω is a subgroup of 𝒫n and A, BϵFm×n then A is equivalent to B relative to Ω if there exists Pϵ𝒫n such that AP=B. In sections 3 and 4, if Ω=𝒫n formulas are given for the number of equivalence classes of a given order and for the total number of classes. In sections 5 and 6 we study two generalizations of the above definition.

Copyright © 1981 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.


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