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arXiv · 1303.2457

Real and complex rank for real symmetric tensors with low ranks

Edoardo Ballico·Alessandra Bernardi
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Abstract

We study the case of a real homogeneous polynomial $P$ whose minimal real and complex decompositions in terms of powers of linear forms are different. We prove that, if the sum of the complex and the real ranks of $P$ is at most $ 3°(P)-1$, then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.

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Edoardo Ballico, Alessandra Bernardi. 2013-03-11. Real and complex rank for real symmetric tensors with low ranks. https://doi.org/10.1155/2013%2F794054

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