RESEARCH ARTICLE

Best rank one approximation of real symmetric tensors can be chosen symmetric

  • Shmuel FRIEDLAND
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  • Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

Received date: 24 May 2012

Accepted date: 19 Oct 2012

Published date: 01 Feb 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We show that a best rank one approximation to a real symmetric tensor, which in principle can be nonsymmetric, can be chosen symmetric. Furthermore, a symmetric best rank one approximation to a symmetric tensor is unique if the tensor does not lie on a certain real algebraic variety.

Cite this article

Shmuel FRIEDLAND . Best rank one approximation of real symmetric tensors can be chosen symmetric[J]. Frontiers of Mathematics in China, 2013 , 8(1) : 19 -40 . DOI: 10.1007/s11464-012-0262-x

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