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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Tokyo :
Springer Japan : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Colección: | JSS Research Series in Statistics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
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| 001 | 978-4-431-55459-2 | ||
| 003 | DE-He213 | ||
| 005 | 20220114122144.0 | ||
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| 008 | 160318s2016 ja | s |||| 0|eng d | ||
| 020 | |a 9784431554592 |9 978-4-431-55459-2 | ||
| 024 | 7 | |a 10.1007/978-4-431-55459-2 |2 doi | |
| 050 | 4 | |a QA276-280 | |
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| 100 | 1 | |a Sakata, Toshio. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Algebraic and Computational Aspects of Real Tensor Ranks |h [electronic resource] / |c by Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Tokyo : |b Springer Japan : |b Imprint: Springer, |c 2016. | |
| 300 | |a VIII, 108 p. 5 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a JSS Research Series in Statistics, |x 2364-0065 | |
| 505 | 0 | |a Basics of Tensor Rank -- 3-Tensors -- Simple Evaluation Methods of Tensor Rank -- Absolutely Nonsingular Tensors and Determinantal Polynomials -- Maximal Ranks -- Typical Ranks -- Global Theory of Tensor Ranks -- 2 × 2 × · · · × 2 Tensors. | |
| 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. | ||
| 650 | 0 | |a Statistics . | |
| 650 | 0 | |a Mathematical statistics-Data processing. | |
| 650 | 0 | |a Social sciences-Statistical methods. | |
| 650 | 1 | 4 | |a Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. |
| 650 | 2 | 4 | |a Statistics and Computing. |
| 650 | 2 | 4 | |a Statistics in Social Sciences, Humanities, Law, Education, Behavorial Sciences, Public Policy. |
| 700 | 1 | |a Sumi, Toshio. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Miyazaki, Mitsuhiro. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9784431554585 |
| 776 | 0 | 8 | |i Printed edition: |z 9784431554608 |
| 830 | 0 | |a JSS Research Series in Statistics, |x 2364-0065 | |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||