# Moore determinant

From Citizendium, the Citizens' Compendium

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

or

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

## References

- David Goss (1996).
*Basic Structures of Function Field Arithmetic*. Springer Verlag. ISBN 3-540-63541-6. Chapter 1.