Hyperdeterminants
Take \(A\) a square matrix \(n\times n\), it is well known that the determinant is a homogeneous polynomial in the coefficients of the matrix. Now consider a hypercubic matrix \(n_ 1\times n_ 2\times\cdots\times n_ k\), is it possible to define the determinant in this case? Using Projective Algebraic Geometry the authors can define the hyperdeterminant of this hypercubic matrix. It is a polynomial if some conditions on \(n_ 1,n_ 2,\dots,n_ k\) are given. Some properties of the hyperdeterminant are studied but there are many open problems in this new theory.
scientific article; zbMATH DE number 221236
scientific article