Partitions of a skew matrix over a finite field
A. Duane Porter, Nick Mousouris · Linear and Multilinear Algebra · 1985
Let GF(pw ) denote a finite field with pw elementsp odd. In this paper formulas are given for calculating the number of solutions X1 , … Xn over GF(q) of matrix equations of the form where B is a skew matrix and the prime denotes transpose. The case in which the ranks of the Xv 1 i n,are specified as arbitrary, but fixed, as well as the case in which the ranks are not specified are both discussed. The number of partitions of certain skew matrices B into a sum of h matrix products, where each product has the form is also discussed.