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 sho
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Toshio Sakata Toshio Sumi Mitsuhiro Miyazaki
Algebraic and Computational Aspects of Real Tensor Ranks 123
SpringerBriefs in Statistics JSS Research Series in Statistics
Editors-in-chief Naoto Kunitomo Akimichi Takemura Series editors Genshiro Kitagawa Manabu Iwasaki Tomoyuki Higuchi Nakahiro Yoshida Yutaka Kano Toshimitsu Hamasaki Shigeyuki Matsui
The current research of statistics in Japan has expanded in several directions in line with recent trends in academic activities in the area of statistics and statistical sciences over the globe. The core of these research activities in statistics in Japan has been the Japan Statistical Society (JSS). This society, the oldest and largest academic organization for statistics in Japan, was founded in 1931 by a handful of pioneer statisticians and economists and now has a history of about 80 years. Many distinguished scholars have been members, including the influential statistician Hirotugu Akaike, who was a past president of JSS, and the notable mathematician Kiyosi Itô, who was an earlier member of the Institute of Statistical Mathematics (ISM), which has been a closely related organization since the establishment of ISM. The society has two academic journals: the Journal of the Japan Statistical Society (English Series) and the Journal of the Japan Statistical Society (Japanese Series). The membership of JSS consists of researchers, teachers, and professional statisticians in many different fields including mathematics, statistics, engineering, medical sciences, government statistics, economics, business, psychology, education, and many other natural, biological, and social sciences. The JSS Series of Statistics aims to publish recent results of current research activities in the areas of statistics and statistical sciences in Japan that otherwise would not be available in English; they are complementary to the two JSS academic journals, both English and Japanese. Because the scope of a research paper in academic journals inevitably has become narrowly focused and condensed in recent years, this series is intended to fill the gap between academic research activities and the form of a single academic paper. The series will be of great interest to a wide audience of researchers, teachers, professional statisticians, and graduate students in many countries who are interested in statistics and statistical sciences, in statistical theory, and in various areas of statistical applications.
More information about this series at http://www.springer.com/series/13497
Toshio Sakata Toshio Sumi Mitsuhiro Miyazaki •
Algebraic and Computational Aspects of Real Tensor Ranks
123
Mitsuhiro Miyazaki Department of Mathematics Kyoto University of Education Kyoto Japan
Toshio Sakata Faculty of Design Kyushu University Fukuoka Japan Toshio Sumi Faculty of Arts and Science Kyushu University Fukuoka Japan
ISSN 2191-544X SpringerBriefs in Statistics ISSN 2364-0057 JSS Research Series in Statistics ISBN 978-4-431-55458-5 DOI 10.1007/978-4-431-55459-2
ISSN 2191-5458
(electronic)
ISS
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