Gram determinants of real binary tensors
A binary tensor consists of 2 n entries arranged into hypercube format 2 × 2 × ⋯ × 2. There are n ways to flatten such a tensor into a matrix of size 2 × 2 n-1. For each flattening, M, we take the determinant of its Gram matrix, det(MMT ). We consider the map that sends a tensor to its n-tuple of Gr...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2018
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| _version_ | 1797103578696908800 |
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| author | Seigal, A |
| author_facet | Seigal, A |
| author_sort | Seigal, A |
| collection | OXFORD |
| description | A binary tensor consists of 2 n entries arranged into hypercube format 2 × 2 × ⋯ × 2. There are n ways to flatten such a tensor into a matrix of size 2 × 2 n-1. For each flattening, M, we take the determinant of its Gram matrix, det(MMT ). We consider the map that sends a tensor to its n-tuple of Gram determinants. We propose a semi-algebraic characterization of the image of this map. This offers an answer to a question raised by Hackbusch and Uschmajew concerning the higher-order singular values of tensors. |
| first_indexed | 2024-03-07T06:22:06Z |
| format | Journal article |
| id | oxford-uuid:f30b1a8d-6d39-4dde-8301-25461134485e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:22:06Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:f30b1a8d-6d39-4dde-8301-25461134485e2022-03-27T12:09:00ZGram determinants of real binary tensorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f30b1a8d-6d39-4dde-8301-25461134485eEnglishSymplectic Elements at OxfordElsevier2018Seigal, AA binary tensor consists of 2 n entries arranged into hypercube format 2 × 2 × ⋯ × 2. There are n ways to flatten such a tensor into a matrix of size 2 × 2 n-1. For each flattening, M, we take the determinant of its Gram matrix, det(MMT ). We consider the map that sends a tensor to its n-tuple of Gram determinants. We propose a semi-algebraic characterization of the image of this map. This offers an answer to a question raised by Hackbusch and Uschmajew concerning the higher-order singular values of tensors. |
| spellingShingle | Seigal, A Gram determinants of real binary tensors |
| title | Gram determinants of real binary tensors |
| title_full | Gram determinants of real binary tensors |
| title_fullStr | Gram determinants of real binary tensors |
| title_full_unstemmed | Gram determinants of real binary tensors |
| title_short | Gram determinants of real binary tensors |
| title_sort | gram determinants of real binary tensors |
| work_keys_str_mv | AT seigala gramdeterminantsofrealbinarytensors |