Decomposability of Tensors
Tensor decomposition is a relevant topic, both for theoretical and applied mathematics, due to its interdisciplinary nature, which ranges from multilinear algebra and algebraic geometry to numerical analysis, algebraic statistics, quantum physics, signal processing, artificial intelligence, etc. The...
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| Format: | Online |
| Jezik: | angleščina |
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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| Online dostop: | 32234 |
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| _version_ | 1869515745896955904 |
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| author | Luca Chiantini (Ed.) |
| author_browse | Luca Chiantini (Ed.) |
| author_facet | Luca Chiantini (Ed.) |
| author_sort | Luca Chiantini (Ed.) |
| collection | Directory of Open Access Books |
| description | Tensor decomposition is a relevant topic, both for theoretical and applied mathematics, due to its interdisciplinary nature, which ranges from multilinear algebra and algebraic geometry to numerical analysis, algebraic statistics, quantum physics, signal processing, artificial intelligence, etc. The starting point behind the study of a decomposition relies on the idea that knowledge of elementary components of a tensor is fundamental to implement procedures that are able to understand and efficiently handle the information that a tensor encodes. Recent advances were obtained with a systematic application of geometric methods: secant varieties, symmetries of special decompositions, and an analysis of the geometry of finite sets. Thanks to new applications of theoretic results, criteria for understanding when a given decomposition is minimal or unique have been introduced or significantly improved. New types of decompositions, whose elementary blocks can be chosen in a range of different possible models (e.g., Chow decompositions or mixed decompositions), are now systematically studied and produce deeper insights into this topic. The aim of this Special Issue is to collect papers that illustrate some directions in which recent researches move, as well as to provide a wide overview of several new approaches to the problem of tensor decomposition. |
| format | Online |
| id | doab-20.500.12854ir-44618 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-446182023-12-20T18:40:40Z Decomposability of Tensors Luca Chiantini (Ed.) QA1-939 QC1-999 border rank and typical rank Tensor analysis Rank Complexity bic Book Industry Communication::P Mathematics & science Tensor decomposition is a relevant topic, both for theoretical and applied mathematics, due to its interdisciplinary nature, which ranges from multilinear algebra and algebraic geometry to numerical analysis, algebraic statistics, quantum physics, signal processing, artificial intelligence, etc. The starting point behind the study of a decomposition relies on the idea that knowledge of elementary components of a tensor is fundamental to implement procedures that are able to understand and efficiently handle the information that a tensor encodes. Recent advances were obtained with a systematic application of geometric methods: secant varieties, symmetries of special decompositions, and an analysis of the geometry of finite sets. Thanks to new applications of theoretic results, criteria for understanding when a given decomposition is minimal or unique have been introduced or significantly improved. New types of decompositions, whose elementary blocks can be chosen in a range of different possible models (e.g., Chow decompositions or mixed decompositions), are now systematically studied and produce deeper insights into this topic. The aim of this Special Issue is to collect papers that illustrate some directions in which recent researches move, as well as to provide a wide overview of several new approaches to the problem of tensor decomposition. 2021-02-11T11:02:51Z 2021-02-11T11:02:51Z 2019-02-15 09:41:46 2019 book 32234 9783038975915 9783038975908 https://directory.doabooks.org/handle/20.500.12854/44618 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.mdpi.com/books/pdfview/book/1139 https://play.google.com/books/publish/a/14935057684283403269#details/ISBN:9783038975908 https://www.mdpi.com/books/pdfview/book/1139 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03897-591-5 10.3390/books978-3-03897-591-5 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783038975915 9783038975908 160 open access |
| spellingShingle | QA1-939 QC1-999 border rank and typical rank Tensor analysis Rank Complexity bic Book Industry Communication::P Mathematics & science Luca Chiantini (Ed.) Decomposability of Tensors |
| title | Decomposability of Tensors |
| title_full | Decomposability of Tensors |
| title_fullStr | Decomposability of Tensors |
| title_full_unstemmed | Decomposability of Tensors |
| title_short | Decomposability of Tensors |
| title_sort | decomposability of tensors |
| topic | QA1-939 QC1-999 border rank and typical rank Tensor analysis Rank Complexity bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 QC1-999 border rank and typical rank Tensor analysis Rank Complexity bic Book Industry Communication::P Mathematics & science |
| url | 32234 |
| work_keys_str_mv | AT lucachiantinied decomposabilityoftensors |