On the rank $1$ decompositions of symmetric tensors

Edoardo Ballico

Abstract


Here we study the uniqueness of a representation of a homogeneous polynomialas a sum of a small number of powers of linear forms (equivalently, a representation of a symmetric tensoras a sum of powers) or (when it is not unique) describe all such additive decompositions. We requirea linear upper bound for the number of addenda with respect to the degree of the polynomial and, for someresults, assumptions like linearly general position.

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Edoardo Ballico, On the rank $1$ decompositions of symmetric tensors, Journal of Mathematical and Computational Science, Vol 2, No 2 (2012), 394-412

Copyright © 2012 Edoardo Ballico. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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