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Moore determinant

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In linear algebra, a Moore matrix, named after E. H. Moore, is a determinant defined over a finite field from a square Moore matrix. A Moore matrix has successive powers of the Frobenius automorphism applied to the first column, i.e., an m × n matrix


for all indices i and j. (Some authors use the transpose of the above matrix.)

The Moore determinant of a square Moore matrix (so m=n) can be expressed as:

where c runs over a complete set of direction vectors, made specific by having the last non-zero entry equal to 1.

See also