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Algebraic and Computational Aspects of Real Tensor Ranks

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.

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Detail Information
Series Title
SpringerBriefs in Statistics
Call Number
519.5 SAK a
Publisher
Tokyo : Springer Tokyo.,
Collation
VIII, 108
Language
English
ISBN/ISSN
978-4-431-55459-2
Classification
519.5
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
Ed. 1
Subject(s)
Computer Science
Statistics in Engineering
Specific Detail Info
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Statement of Responsibility
Other Information
Cataloger
umi
Source
https://link.springer.com/content/pdf/10.1007/978-4-431-55459-2.pdf?pdf=button
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