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
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.
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