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作者 Sakata, Toshio, author
書名 Algebraic and computational aspects of real tensor ranks / by Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki
出版項 Tokyo : Springer Japan : Imprint: Springer, 2016
國際標準書號 9784431554592 (electronic bk.)
9784431554585 (paper)
國際標準號碼 10.1007/978-4-431-55459-2 doi
book jacket
說明 1 online resource (viii, 108 pages) : illustrations, digital ; 24 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
系列 SpringerBriefs in statistics, 2191-544X
SpringerBriefs in statistics
附註 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
Host Item Springer eBooks
主題 Calculus of tensors
Ranking and selection (Statistics)
Statistics
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
Statistics and Computing/Statistics Programs
Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law
Alt Author Sumi, Toshio, author
Miyazaki, Mitsuhiro, author
SpringerLink (Online service)
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