The Number of Eigenvalues of a Tensor

Details The Number of Eigenvalues of a Tensor The Number of Eigenvalues of a Tensor

2010-04-28

arxiv.org/abs/1004.4953v2

Mathematics

Numerical Analysis

12 pages, fixed several typos

Scientific paper

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.

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