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

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.

Keywords

Symmetric tensor / rank one approximation of tensors / uniqueness of rank one approximation

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