The rank of a 2 × 2 × 2 tensor
| Autor: | Carla D. Martin |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Linear and Multilinear Algebra. 59:943-950 |
| ISSN: | 1563-5139 0308-1087 |
| Popis: | As computing power increases, many more problems in engineering and data analysis involve computation with tensors, or multi-way data arrays. Most applications involve computing a decomposition of a tensor into a linear combination of rank-1 tensors. Ideally, the decomposition involves a minimal number of terms, i.e. computation of the rank of the tensor. Tensor rank is not a straight-forward extension of matrix rank. A constructive proof based on an eigenvalue criterion is provided that shows when a 2 × 2 × 2 tensor over ℝ is rank-3 and when it is rank-2. The results are extended to show that n × n × 2 tensors over ℝ have maximum possible rank n + k where k is the number of complex conjugate eigenvalue pairs of the matrices forming the two faces of the tensor cube. |
| Databáze: | OpenAIRE |
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