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Tensor RankPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. , 71 p.
##### Keyword [en]

generic rank, symmetric tensor, tensor rank, tensors over finite fields, typical rank
##### Keyword [sv]

generisk rang, symmetrisk tensor, tensorrang, tensorer över ändliga kroppar, typisk rang
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-78449ISRN: LiTH-MAI-EX--2012/06--SEOAI: oai:DiVA.org:liu-78449DiVA: diva2:551672
##### Subject / course

Applied Mathematics; Mathematics
##### Presentation

2012-06-11, BL31, Linköpings universitet, Linköping, 13:15 (Swedish)
##### Uppsok

Physics, Chemistry, Mathematics

#####

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##### Examiners

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Available from: 2012-09-27 Created: 2012-06-12 Last updated: 2012-09-27Bibliographically approved

This master's thesis addresses numerical methods of computing the typical ranks of tensors over the real numbers and explores some properties of tensors over finite fields.

We present three numerical methods to compute typical tensor rank. Two of these have already been published and can be used to calculate the lowest typical ranks of tensors and an approximate percentage of how many tensors have the lowest typical ranks (for some tensor formats), respectively. The third method was developed by the authors with the intent to be able to discern if there is more than one typical rank. Some results from the method are presented but are inconclusive.

In the area of tensors over nite filds some new results are shown, namely that there are eight GL_{q}(2) GL_{q}(2) GL_{q}(2)-orbits of 2 2 2 tensors over any finite field and that some tensors over Fq have lower rank when considered as tensors over F_{q}2 . Furthermore, it is shown that some symmetric tensors over F2 do not have a symmetric rank and that there are tensors over some other finite fields which have a larger symmetric rank than rank.