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We provide simple criteria and algorithms for expressing homogeneouspolynomials as sums of powers of independent linear forms, or equivalently, fordecomposing symmetric tensors into sums of rank-1 symmetric tensors of linearlyindependent vectors. The criteria rely on two facets of higher degree forms,namely Harrison's algebraic theory and some algebro-geometric properties. Theproposed algorithms are elementary and based purely on solving linear andquadratic equations. Moreover, as a byproduct of our criteria and algorithmsone can easily decide whether or not a homogeneous polynomial or symmetrictensor is orthogonally or unitarily decomposable.

Diagonalizable Higher Degree Forms and Symmetric Tensors