Singular hypersurfaces and multilinear algebra (Q1807495)

The paper investigates determinants of multidimensional matrices and a multidimensional eigenvalue theory. The author shows how the invariants of n-ary forms can be produced from the discriminants of multilinear forms (determinants of multidimensional matrices), which should be considered as a generalization of the classical Hessians and resultants, and develops a technique which gives an algorithm for calculating the discriminants of multilinear forms. He establishes the degeneracy of a \(d\)-linear form in terms of the structure of the set of critical points of the corresponding homogeneous polynomial function. Finally, the example of 3-linear forms is illustrated.