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The existence of certain Fq-spaces of differential forms of the projectiveline over a field K containing Fq leads us to prove an identity linking thedeterminant of the Moore matrix of n indeterminates with the determinant of theMoore matrix of the cofactors of its first row. These same spaces give aninterpretation of Elkies pairing in terms of residues of differential forms.This pairing puts in duality the Fq-vector space of the roots of a Fq-linearpolynomial and that of the roots of its reversed polynomial.

On M-O.Ore determinants