The Number of Eigenvalues of a Tensor

Dustin Cartwright, Bernd Sturmfels

Published 2010-04-28, updated 2010-05-14Version 2

Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized eigenvalues of a symmetric tensor is always finite. We also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants.