Convex Hulls of Grassmannians and Combinatorics of Symmetric Hypermatrices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911799506370560 |
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| author | Narita, Kazumasa |
| author_facet | Narita, Kazumasa |
| contents | It is known that the complex Grassmannian of $k$-dimensional subspaces can be identified with the set of projection matrices of rank $k$. It is also classically known that the convex hull of this set is the set of Hermitian matrices with eigenvalues between $0$ and $1$ and summing to $k$. We give a new proof of this fact. We also give an existence theorem for a certain combinatorial class of hypermatrices by a similar argument. This existence theorem can be rewritten into an existence theorem for a uniform weighted hypergraph with given weighted degree sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06953 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convex Hulls of Grassmannians and Combinatorics of Symmetric Hypermatrices Narita, Kazumasa Combinatorics 05B20, 52A37 It is known that the complex Grassmannian of $k$-dimensional subspaces can be identified with the set of projection matrices of rank $k$. It is also classically known that the convex hull of this set is the set of Hermitian matrices with eigenvalues between $0$ and $1$ and summing to $k$. We give a new proof of this fact. We also give an existence theorem for a certain combinatorial class of hypermatrices by a similar argument. This existence theorem can be rewritten into an existence theorem for a uniform weighted hypergraph with given weighted degree sequence. |
| title | Convex Hulls of Grassmannians and Combinatorics of Symmetric Hypermatrices |
| topic | Combinatorics 05B20, 52A37 |
| url | https://arxiv.org/abs/2204.06953 |