Published May 2, 2012
| Version v1
Publication
Real and complex rank for real symmetric tensors with low complex symmetric rank
Creators
Contributors
Others:
- University of Trento [Trento]
- Geometry, algebra, algorithms (GALAAD) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- The authors were partially supported by CIRM of FBK Trento (Italy), Project Galaad of INRIA Sophia Antipolis Méditerranée (France), Marie Curie: Promoting science (FP7-PEOPLE- 2009-IEF), MIUR and GNSAGA of INdAM (Italy
- European Project: 252367,EC:FP7:PEOPLE,FP7-PEOPLE-2009-IEF,DECONSTRUCT(2010)
Description
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.
Additional details
Identifiers
- URL
- https://hal.inria.fr/hal-00693413
- URN
- urn:oai:HAL:hal-00693413v1
Origin repository
- Origin repository
- UNICA