The Cullis' determinant as Pfaffian
Abstract
The Cullis' determinant is a generalization of the ordinary determinant for rectangular matrices. It is defined as the alternating sum of maximal minors of given matrix. In this paper we express the Cullis' determinant of a matrix X as the Pfaffian of the matrix obtained from X by matrix multiplication and transposition. Relying on this result, we present an efficient polynomial-time algorithm for calculating the Cullis' determinant of given matrix.
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