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Algebraic and computational aspects ...

Sakata, Toshio.

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Algebraic and computational aspects of real tensor ranks

紀錄類型:	書目-電子資源 : Monograph/item
正題名/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. -
電子資源:	http://dx.doi.org/10.1007/978-4-431-55459-2
ISBN:	9784431554592

Algebraic and computational aspects of real tensor ranks
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:

533863
Calculus of tensors.

LC Class. No.: QA433

Dewey Class. No.: 515.63

Algebraic and computational aspects of real tensor ranks
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520 $a 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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