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 deg(P) − 1, then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.
Real and complex rank for real symmetric tensors with low ranks / Ballico, Edoardo; Bernardi, Alessandra. - In: ALGEBRA. - ISSN 2314-4106. - STAMPA. - 2013:(2013), pp. 794054.1-794054.55. [10.1155/2013/794054]
Real and complex rank for real symmetric tensors with low ranks
Ballico, Edoardo;Bernardi, Alessandra
2013-01-01
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 deg(P) − 1, then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.File in questo prodotto:
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