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Dimension Bounds for Constant Rank Subspaces of Symmetric Bilinear Forms over a Finite Field
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Dimension bounds for constant rank subspaces of symmetric bilinear forms over a finite field
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A dimension bound for constant rank subspaces of matrices over a finite field
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2015 |
| Abstract | K be a field and let m and n be positive integers, where m does not exceed n. We say that a non-zero subspace of m x n matrices over K is a constant rank r subspace if each non-zero element of the subspace has rank r, where r is a positive integer that does not exceed m. We show in this paper that if K is a finite field containing at least r+1 elements, any constant rank r subspace of m x n matrices over K has dimension at most n. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1501.02721v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
