Hyperdeterminant

In algebra, the hyperdeterminant is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an nxn square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or hypermatrix. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the hypermatrix. Many other properties of determinants generalize in some way to hyperdeterminants but unlike a determinant, the hyperdeterminant does not have a simple geometric interpretation in terms of volumes.