Eigenvalues and invariants of tensors (Q854009)

The objective of this paper is to define and develop the concepts of eigenvalues and invariants for tensors of order higher than two. The author represents a higher order tensor by a ``supermatrix'' (in our opinion this denomination is unfortunate since it is already used in superanalysis and supersymmetric theories), defines the concepts of E-eigenvalue, E-eigenvector and E-characteristic polynomial of a tensor, and studies their properties, proving various results and leaving some questions opened. The paper contains several interesting results which may be very useful.