Tensor rank and dimension expanders
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918239523569664 |
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| author | Dvir, Zeev |
| author_facet | Dvir, Zeev |
| contents | We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known explicit constructions. Using these constructions we show that one can construct an explicit $[D]\times [n] \times [n]$-tensor with rank at least $(2 - ε)n$, with $D$ a constant depending on $ε$. Our results extend to border rank over the real or complex numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor rank and dimension expanders Dvir, Zeev Combinatorics Computational Complexity We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known explicit constructions. Using these constructions we show that one can construct an explicit $[D]\times [n] \times [n]$-tensor with rank at least $(2 - ε)n$, with $D$ a constant depending on $ε$. Our results extend to border rank over the real or complex numbers. |
| title | Tensor rank and dimension expanders |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2511.02670 |