Rank classification of tensors over
| Autor: | Stavros G. Stavrou, Nicholas J. Hernandez, Richard M. Low |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Tensor contraction
Algebra and Number Theory Rank (linear algebra) 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Rank of an abelian group Combinatorics Tensor product Cartesian tensor Invariants of tensors Symmetric tensor Tensor 0101 mathematics Mathematics |
| Zdroj: | Linear and Multilinear Algebra. 64:2297-2312 |
| ISSN: | 1563-5139 0308-1087 |
| Popis: | We consider tensors of format over the finite field . We use computer algebra to classify these tensors by their tensor rank, thus determining the maximum tensor rank to be 9. As a corollary, we provide a new upper bound that the maximum rank of an order-n tensor of format , for , over is at most . We also determine that there are 261 canonical forms of the rank 9 (maximum rank) tensors under the action of , the semi-direct product of (a direct product of) general linear groups with the symmetric group on five elements. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|