大葉大學圖書館 |

Algebraic and computational aspects of real tensor ranks[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.63
書名/作者:	Algebraic and computational aspects of real tensor ranks/ by Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki.
作者:	Sakata, Toshio.
其他作者:	Sumi, Toshio.
出版者:	Tokyo : : Springer Japan :, 2016.
面頁冊數:	viii, 108 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Calculus of tensors.
標題:	Ranking and selection (Statistics)
標題:	Statistics.
標題:	Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
標題:	Statistics and Computing/Statistics Programs.
標題:	Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law.
ISBN:	9784431554592
ISBN:	9784431554585
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-4-431-55459-2

Algebraic and computational aspects of real tensor ranks[electronic resource] /
Sakata, Toshio.

Algebraic and computational aspects of real tensor ranks[electronic resource] /by Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki. - Tokyo :Springer Japan :2016. - viii, 108 p. :ill., digital ;24 cm. - SpringerBriefs in statistics,2191-544X. - SpringerBriefs in statistics..

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.

ISBN: 9784431554592

Standard No.: 10.1007/978-4-431-55459-2doiSubjects--Topical Terms:

403530
Calculus of tensors.

LC Class. No.: QA433

Dewey Class. No.: 515.63

Algebraic and computational aspects of real tensor ranks[electronic resource] /
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