Algebraic and Computational Aspects of Real Tensor Ranks
Published on 18. March 2016
VIII, 108 pages
978-4-431-55459-2 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Tokyo
Japan
Publishing group
Springer Tokyo
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
VIII, 108 p. 5 illus.
File size
1,73 MB
ISBN-13
978-4-431-55459-2 (9784431554592)
DOI
10.1007/978-4-431-55459-2
Schweitzer Classification
Other editions
Additional editions
Toshio Sakata | Toshio Sumi | Mitsuhiro Miyazaki
Algebraic and Computational Aspects of Real Tensor Ranks
Book
03/2016
Springer
€53.49
Shipment within 10-15 days
Content
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.
