Diagonalizable Higher Degree Forms and Symmetric Tensors

Abstract

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.

11 pages. Minor revision. Final version to be sumbmitted for publication

References in corpus (1)

• Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective

Cited by in corpus (1)

• On Centers and Direct Sum Decompositions of Higher Degree Forms