Permutation matrices and matrix equivalence over a finite field
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....
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000367 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |