Pfaffian

In mathematics, the determinant of a skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries. This polynomial is called the Pfaffian of the matrix, The term Pfaffian was introduced by Cayley (1852) who named them after Johann Friedrich Pfaff. The Pfaffian is nonvanishing only for 2n × 2n skew-symmetric matrices, in which case it is a polynomial of degree n.