On the ranks of skew-centrosymmetric matrices over finite fields Original Research Article

For any finite field F we determine the number of n by n matrices of skew-centrosymmetric form which are invertible over F. This result is obtained using a unimodality property of the ranks of matrices of this form. As a corollary to this result we count the n by n matrices of skew-centrosymmetric form of any specified rank.