English

The Number of Eigenvalues of a Tensor

Numerical Analysis 2018-06-18 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1004.4953,
  title  = {The Number of Eigenvalues of a Tensor},
  author = {Dustin Cartwright and Bernd Sturmfels},
  journal= {arXiv preprint arXiv:1004.4953},
  year   = {2018}
}

Comments

12 pages, fixed several typos