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.
Edoardo Ballico, Alessandra Bernardi (2013). Real and Complex Rank for Real Symmetric Tensors with Low Ranks. ALGEBRA, 2013, 1-5 [10.1155/2013/794054].
Real and Complex Rank for Real Symmetric Tensors with Low Ranks
BERNARDI, ALESSANDRA
2013
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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