rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Toward a classification of the ranks and border ranks of all (3,3,3) trilinear forms
  name:
    name part: Allums, Derek James.
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: The study of the ranks and border ranks of tensors is an active area of research. By the example of determining the complexity of matrix multiplication I introduce the reader to the notion of the rank and border rank of a tensor. Then, after presenting basic preliminary material from algebraic geometry and multilinear algebra,I quantify precisely what it means for some tensor to be of given rank, border rank,symmetric rank or symmetric rank. Objects of a given (symmetric) border rank are then interpreted geometrically as elements of certain secant varieties of Veronese and Segre varieties. Using this, I describe some of the techniques used to arrive at the classification of all (3,3,3) presented by Kok Omn Ng. The main result of this thesis is a classification of all the border ranks and some of the ranks of the 24 normal forms given by Kok Omn NG in "The Classification of (3,3,3) trilinear forms".
  note: by Derek James Allums.
  note: "Major Subject: Mathematics"
  note: Title from author supplied metadata (automated record created 2011-08-09 15:12:36).
  note: Electronic resource.
  note: Bachelor of Science Texas A&M University 2011 http://hdl.handle.net/1969.1/ETD-TAMU-2011-05-9621
  note: Includes bibliographical references.
  note: Text (Undergraduate thesis)
  subject:
    topic: Major mathematics
  subject:
    topic: Tensor border rank
  subject:
    topic: Trilinear forms
  subject:
    topic: Tensor rank
  subject:
    topic: Algebraic geometry
  subject:
    topic: Algebra
  identifier: http://hdl.handle.net/1969.1/ETD-TAMU-2011-05-9621
  record info:
    record content source: TXA
    record creation date: 110818
    record change date: 20151202142310.0
    record identifier: in00002717739