Diagonalizable Higher Degree Forms and Symmetric Tensors

Autor:	Huang, Hua-Lin, Lu, Huajun, Ye, Yu, Zhang, Chi
Rok vydání:	2020
Předmět:	Mathematics - Rings and Algebras Mathematics - Commutative Algebra 15A69 14J70 11E76
Zdroj:	Linear Alg. Appl. 613 (2021) 151--169
Druh dokumentu:	Working Paper
DOI:	10.1016/j.laa.2020.12.018
Popis:	We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent vectors. The criteria rely on two facets of higher degree forms, namely Harrison's algebraic theory and some algebro-geometric properties. The proposed algorithms are elementary and based purely on solving linear and quadratic equations. Moreover, as a byproduct of our criteria and algorithms one can easily decide whether or not a homogeneous polynomial or symmetric tensor is orthogonally or unitarily decomposable. Comment: 11 pages. Minor revision. Final version to be sumbmitted for publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.08041 Zobrazit plný text záznamu View this record from Arxiv