Function Repository Resource:

# HyperDet

Compute the hyperdeterminant for a given hypermatrix (a multidimensional array of complex numbers)

Contributed by: Riccardo Gatti
 ResourceFunction["HyperDet"][h] gives the hyperdeterminant of the cubical hypermatrix (or hypercubical) h.

## Details

A 2-dimensional n×n=n2 square matrix is a particular case of the more general d-dimensional n××n=nd cubical hypermatrix (d-hypermatrix), hence the hyperdeterminant is a more general form of the determinant. There are two ways to generalize the determinant to hyperdeterminant: the combinatorial way and the geometric way.
Let A be a d-hypermatrix. The combinatorial hyperdeterminant of A is defined as where Sn is the set symmetric group on n letters and sgn is the permutation signature function.
There is also a definition with a geometric interpretation.

## Examples

### Basic Examples (1)

The hyperdeterminant of a cubical hypermatrix where d=4 and n=2:

 In[1]:=
 Out[1]=

Riccardo Gatti

## Version History

• 1.0.0 – 18 November 2022