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: Algebraic and Computational Aspects of Real Tensor Ranks
  name:
    name part: Sakata, Toshio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Sumi, Toshio.
    role:
      role term: author.
  name:
    name part: Miyazaki, Mitsuhiro.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ja
    date issued: 2016
    edition: 1st ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 108 p. 5 illus. online resource.
  abstract: This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.
  table of contents: Basics of Tensor Rank -- 3-Tensors -- Simple Evaluation Methods of Tensor Rank -- Absolutely Nonsingular Tensors and Determinantal Polynomials -- Maximal Ranks -- Typical Ranks -- Global Theory of Tensor Ranks -- 2 × 2 × · · · × 2 Tensors.
  note: by Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki.
  subject:
    topic: Statistics
  subject:
    topic: Statistics
  subject:
    topic: Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
  subject:
    topic: Statistics and Computing/Statistics Programs
  subject:
    topic: Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law
  classification: QA276-280
  classification: 519.5
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Statistics
  identifier: 9784431554592
  identifier: http://dx.doi.org/10.1007/978-4-431-55459-2
  record info:
    record creation date: 160318
    record change date: 20160318113716.0
    record identifier: 978-4-431-55459-2