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Tensor Rank
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

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 GLq(2) GLq(2) GLq(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 Fq2 . 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.

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

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Erdtman, EliasJönsson, Carl
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
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  • vancouver
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More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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