For a linear operator, this function acting on the operator minus a variable times the identity gives the characteristic polynomial of the operator.
In some cases, this function can be expressed as the square of a polynomial known as the Pfaffian. The content of a simplex can be calculated using the one named for a man who showed that every group is isomorphic to a subgroup of a permutation group and a man who developed a 3D generalization of the Sierpinski carpet. It can be characterized as the alternating, n-linear function which returns 1 for the identity. For a linear operator, this function acting on the operator minus a variable times the identity gives the characteristic polynomial of the operator. It can be calculated using the method of cofactor expansion, and it can be used to solve a system of linear equations by Cramer's rule. FTP, name this function which, for a 2 by 2 matrix a b c d, is equal to a d minus b c.
In some cases, this function can be expressed as the square of a polynomial known as the Pfaffian.
{determinant}