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Best rank-k approximations for tensors: generalizing Eckart-Young
dc.contributor.author | Tocino-Sánchez, Alicia | |
dc.date.accessioned | 2020-02-03T08:20:42Z | |
dc.date.available | 2020-02-03T08:20:42Z | |
dc.date.created | 2020 | |
dc.date.issued | 2020-02-03 | |
dc.identifier.uri | https://hdl.handle.net/10630/19237 | |
dc.description.abstract | Joint work with Jan Draisma and Giorgio Ottaviani. Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distance function from f to the set of tensors of rank at most k, which we call the critical rank-at-most-k tensors for f. When f is a matrix, the critical rank-one matrices for f correspond to the singular pairs of f . The critical rank-one tensors for f lie in a linear subspace H_f, the critical space of f. Our main result is that, for any k, the critical rank-at-most-k tensors for a sufficiently general f also lie in the critical space H_f. This is the part of Eckart-Young Theorem that generalizes from matrices to tensors. Moreover, we show that when the tensor format satisfies the triangle inequalities, the critical space H_f is spanned by the complex critical rank-one tensors. Since f itself belongs to H_f, we deduce that also f itself is a linear combination of its critical rank-one tensors. For simplicity, we will focus on binary forms during the talk. | en_US |
dc.description.sponsorship | Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. | en_US |
dc.language.iso | eng | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Matemáticas | en_US |
dc.subject | Tensores (Álgebra) | en_US |
dc.subject.other | Tensores euclideanos | en_US |
dc.title | Best rank-k approximations for tensors: generalizing Eckart-Young | en_US |
dc.type | info:eu-repo/semantics/conferenceObject | en_US |
dc.relation.eventtitle | V Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española- Castelló 2020 | en_US |
dc.relation.eventplace | Castelló, España | en_US |
dc.relation.eventdate | 01/2020 | en_US |