Permutation Matrices and Matrix Equivalence Over a Finite Field

Gary L. Mullen

Research output: Contribution to journalArticlepeer-review

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, BɛFm×n then A is equivalent to B relative to Ω if there exists ΡεΡn 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.

Original languageEnglish (US)
Pages (from-to)503-512
Number of pages10
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume4
Issue number3
DOIs
StatePublished - 1981

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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