# Real and complex rank for real symmetric tensors with low complex symmetric rank

2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We study the case of real homogeneous polynomial $P$ whose minimal real and complex decompositions in terms of powers of linear forms are different. In particularly we will show that, if the sum of the complex and the real ranks of $P$ is smaller or equal than $3\deg(P)-1$, then the difference of the two decompositions is completely determined either on a line or on a conic.
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Preprints, Working Papers, ...

Cited literature [18 references]

https://hal.inria.fr/hal-00693413
Contributor : Alessandra Bernardi <>
Submitted on : Wednesday, May 2, 2012 - 4:13:26 PM
Last modification on : Thursday, January 11, 2018 - 4:14:55 PM
Long-term archiving on : Friday, August 3, 2012 - 2:46:23 AM

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realcRank0512.pdf
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• HAL Id : hal-00693413, version 1

### Citation

Edoardo Ballico, Alessandra Bernardi. Real and complex rank for real symmetric tensors with low complex symmetric rank. 2012. ⟨hal-00693413⟩

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