Matches in SemOpenAlex for { <https://semopenalex.org/work/W3178793911> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W3178793911 abstract "We build a combinatorial technique to solve several long standing problems in linear algebra with a particular focus on algorithmic complexity of matrix completion and tensor decomposition problems. For all appropriate integral domains R, we show the polynomial time equivalence of the problem of the solvability of a system of polynomial equations over R to • the minimum rank matrix completion problem (in particular, we answer a question asked by Buss, Frandsen, Shallit in 1999), • the determination of matrix rigidity (we answer a question posed by Mahajan, Sarma in 2010 by showing the undecidability over Z, and we solve recent problems of Ramya corresponding to Q and R), • the computation of tensor rank (we answer a question asked by Gonzalez, Ja'Ja' in 1980 on the undecidability over Z, and, additionally, the special case with R = Q solves a problem posed by Blaser in 2014), • the computation of the symmetric rank of a symmetric tensor, whose algorithimic complexity remained open despite an extensive discussion in several foundational papers. In particular, we prove the NP-hardness conjecture proposed by Hillar, Lim in 2013. In addition, we solve two problems on fractional minimal ranks of incomplete matrices recently raised by Grossmann, Woerdeman, and we answer, in a strong form, a recent question of Babai, Kivva on the dependence of the solution to the matrix rigidity problem on the choice of the target field." @default.
- W3178793911 created "2021-07-19" @default.
- W3178793911 creator A5021579450 @default.
- W3178793911 date "2021-07-01" @default.
- W3178793911 modified "2023-09-23" @default.
- W3178793911 title "How Hard is the Tensor Rank" @default.
- W3178793911 hasPublicationYear "2021" @default.
- W3178793911 type Work @default.
- W3178793911 sameAs 3178793911 @default.
- W3178793911 citedByCount "0" @default.
- W3178793911 crossrefType "posted-content" @default.
- W3178793911 hasAuthorship W3178793911A5021579450 @default.
- W3178793911 hasConcept C106487976 @default.
- W3178793911 hasConcept C11413529 @default.
- W3178793911 hasConcept C114614502 @default.
- W3178793911 hasConcept C118615104 @default.
- W3178793911 hasConcept C120665830 @default.
- W3178793911 hasConcept C121332964 @default.
- W3178793911 hasConcept C134306372 @default.
- W3178793911 hasConcept C136119220 @default.
- W3178793911 hasConcept C155281189 @default.
- W3178793911 hasConcept C159985019 @default.
- W3178793911 hasConcept C164226766 @default.
- W3178793911 hasConcept C192209626 @default.
- W3178793911 hasConcept C192562407 @default.
- W3178793911 hasConcept C20178491 @default.
- W3178793911 hasConcept C202444582 @default.
- W3178793911 hasConcept C2780069185 @default.
- W3178793911 hasConcept C33923547 @default.
- W3178793911 hasConcept C45374587 @default.
- W3178793911 hasConcept C520416788 @default.
- W3178793911 hasConceptScore W3178793911C106487976 @default.
- W3178793911 hasConceptScore W3178793911C11413529 @default.
- W3178793911 hasConceptScore W3178793911C114614502 @default.
- W3178793911 hasConceptScore W3178793911C118615104 @default.
- W3178793911 hasConceptScore W3178793911C120665830 @default.
- W3178793911 hasConceptScore W3178793911C121332964 @default.
- W3178793911 hasConceptScore W3178793911C134306372 @default.
- W3178793911 hasConceptScore W3178793911C136119220 @default.
- W3178793911 hasConceptScore W3178793911C155281189 @default.
- W3178793911 hasConceptScore W3178793911C159985019 @default.
- W3178793911 hasConceptScore W3178793911C164226766 @default.
- W3178793911 hasConceptScore W3178793911C192209626 @default.
- W3178793911 hasConceptScore W3178793911C192562407 @default.
- W3178793911 hasConceptScore W3178793911C20178491 @default.
- W3178793911 hasConceptScore W3178793911C202444582 @default.
- W3178793911 hasConceptScore W3178793911C2780069185 @default.
- W3178793911 hasConceptScore W3178793911C33923547 @default.
- W3178793911 hasConceptScore W3178793911C45374587 @default.
- W3178793911 hasConceptScore W3178793911C520416788 @default.
- W3178793911 hasLocation W31787939111 @default.
- W3178793911 hasOpenAccess W3178793911 @default.
- W3178793911 hasPrimaryLocation W31787939111 @default.
- W3178793911 hasRelatedWork W1627809037 @default.
- W3178793911 hasRelatedWork W1997400812 @default.
- W3178793911 hasRelatedWork W2038908286 @default.
- W3178793911 hasRelatedWork W2075349905 @default.
- W3178793911 hasRelatedWork W2091834053 @default.
- W3178793911 hasRelatedWork W2391029584 @default.
- W3178793911 hasRelatedWork W2494193747 @default.
- W3178793911 hasRelatedWork W2622765080 @default.
- W3178793911 hasRelatedWork W2743118218 @default.
- W3178793911 hasRelatedWork W2896887339 @default.
- W3178793911 hasRelatedWork W2949976741 @default.
- W3178793911 hasRelatedWork W2963635811 @default.
- W3178793911 hasRelatedWork W2984170573 @default.
- W3178793911 hasRelatedWork W3036836463 @default.
- W3178793911 hasRelatedWork W3097592276 @default.
- W3178793911 hasRelatedWork W3104988765 @default.
- W3178793911 hasRelatedWork W3111019328 @default.
- W3178793911 hasRelatedWork W3135568492 @default.
- W3178793911 hasRelatedWork W3501056 @default.
- W3178793911 hasRelatedWork W40677528 @default.
- W3178793911 isParatext "false" @default.
- W3178793911 isRetracted "false" @default.
- W3178793911 magId "3178793911" @default.
- W3178793911 workType "article" @default.