JSS Research Series in Statistics

Algebraic and Computational Aspects of Real Tensor Ranks

Authors: Sakata, Toshio, Sumi, Toshio, Miyazaki, Mitsuhiro

  • Presents┬áthe first comprehensive treatment of maximal ranks and typical ranks over the real number file
  • Provides interesting ideas of determinant polynomials, determinantal ideals, absolutely nonsingular tensors and absolutely full column rank tensors
  • Includes numerical methods of determining ranks by simultaneous singular value decomposition through a theory of matrix star algebra
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eBook $39.99
price for USA (gross)
  • ISBN 978-4-431-55459-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-4-431-55458-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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 (8 chapters)

  • Basics of Tensor Rank

    Sakata, Toshio (et al.)

    Pages 1-10

  • 3-Tensors

    Sakata, Toshio (et al.)

    Pages 11-15

  • Simple Evaluation Methods of Tensor Rank

    Sakata, Toshio (et al.)

    Pages 17-28

  • Absolutely Nonsingular Tensors and Determinantal Polynomials

    Sakata, Toshio (et al.)

    Pages 29-37

  • Maximal Ranks

    Sakata, Toshio (et al.)

    Pages 39-59

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-4-431-55459-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-4-431-55458-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic and Computational Aspects of Real Tensor Ranks
Authors
Series Title
JSS Research Series in Statistics
Copyright
2016
Publisher
Springer Japan
Copyright Holder
The Author(s)
eBook ISBN
978-4-431-55459-2
DOI
10.1007/978-4-431-55459-2
Softcover ISBN
978-4-431-55458-5
Series ISSN
2364-0057
Edition Number
1
Number of Pages
VIII, 108
Number of Illustrations and Tables
5 b/w illustrations
Topics