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Article overview
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Abelian Tensors | J.M. Landsberg
; Mateusz Michałek
; | Date: |
14 Apr 2015 | Abstract: | We analyze tensors in the tensor product of three m-dimensional vector spaces
satisfying Strassen’s equations for border rank m. Results include: two purely
geometric characterizations of the Coppersmith-Winograd tensor, a reduction to
the study of symmetric tensors under a mild genericity hypothesis, and numerous
additional equations and examples. This study is closely connected to the study
of the variety of m-dimensional abelian subspaces of the space of endomorphisms
of an m-dimensional vector space, and the subvariety consisting of the Zariski
closure of the variety of maximal tori, called the variety of reductions. | Source: | arXiv, 1504.3732 | Services: | Forum | Review | PDF | Favorites |
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