English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the problem of finding orthogonal low-rank approximations ofsymmetric tensors. In the case of matrices, the approximation is a truncatedsingular value decomposition which is then symmetric. Moreover, for rank-oneapproximations of tensors of any dimension, a classical result proven by Banachin 1938 shows that the optimal approximation can always be chosen to besymmetric. In contrast to these results, this article shows that thecorresponding statement is no longer true for orthogonal approximations ofhigher rank. Specifically, for any of the four common notions of tensororthogonality used in the literature, we show that optimal orthogonalapproximations of rank greater than one cannot always be chosen to besymmetric.

Optimal orthogonal approximations to symmetric tensors cannot always be chosen symmetric