Table of Contents
Algebra
Volume 2013, Article ID 794054, 5 pages
http://dx.doi.org/10.1155/2013/794054
Research Article

Real and Complex Rank for Real Symmetric Tensors with Low Ranks

1Department of Mathematics, University of Trento, Povo, 38123 Trento, Italy
2Department of Mathematics “Giuseppe Peano," University of Turin, 10123 Turin, Italy

Received 20 November 2012; Revised 5 February 2013; Accepted 5 February 2013

Academic Editor: Ricardo L. Soto

Copyright © 2013 Edoardo Ballico and Alessandra Bernardi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the case of a real homogeneous polynomial 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 is at most , then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines.