Algebraic and Computational Aspects of Real Tensor Ranks is popular PDF and ePub book, written by Toshio Sakata in 2016-03-18, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Algebraic and Computational Aspects of Real Tensor Ranks can be Read Online from any device for your convenience.
Algebraic and Computational Aspects of Real Tensor Ranks Book PDF Summary
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.
Detail Book of Algebraic and Computational Aspects of Real Tensor Ranks PDF
- Author : Toshio Sakata
- Release : 18 March 2016
- Publisher : Springer
- ISBN : 9784431554592
- Genre : Mathematics
- Total Page : 112 pages
- Language : English
- PDF File Size : 19,8 Mb
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