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

2011/10/26 by Friedland, Shmuel · 3 citations
#15A18 #15A69 #46B28 #65D15 #65H10 #65K10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1110.5689

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.

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