Eigenvectors of tensors and algorithms for Waring decomposition
Algebraic Geometry
2025-10-16 v2
Abstract
A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem).
Keywords
Cite
@article{arxiv.1103.0203,
title = {Eigenvectors of tensors and algorithms for Waring decomposition},
author = {Luke Oeding and Giorgio Ottaviani},
journal= {arXiv preprint arXiv:1103.0203},
year = {2025}
}
Comments
32 pages; three Macaulay2 files as ancillary files. Revised with referee's suggestions. Accepted JSC