Permutation matrices and matrix equivalence over a finite field

Gary L. Mullen

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-10

Abstract:

Let F = G F ( q ) denote the finite field of order q and F m × n the ring of m × n matrices over F . Let 𝒫 n be the set of all permutation matrices of order n over F so that 𝒫 n is ismorphic to S n . If Ω is a subgroup of 𝒫 n and A , B ϵ F m × n then A is equivalent to B relative to Ω if there exists P ϵ 𝒫 n such that A P = B . In sections 3 and 4, if Ω = 𝒫 n 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.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:583823

DOI: 10.1155/S0161171281000367

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