Symmetric matrices defined by plane vector sequences
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908284785524736 |
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| author | Masuda, Mikiya |
| author_facet | Masuda, Mikiya |
| contents | Motivated by a work of Fu-So-Song, we associate a symmetric matrix $A$ to a plane vector sequence $v$ and give a formula to find the signature of $A$ in terms of the sequence $v$. When $A$ is nonsingular, we interpret the relation between $A$ and $A^{-1}$ from a topological viewpoint. Finally, we associate an omnioriented quasitoric orbifold $X$ of real dimension four to the sequence $v$ and show that $A^{-1}$ is the intersection matrix of the characteristic suborbifolds of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric matrices defined by plane vector sequences Masuda, Mikiya Combinatorics Algebraic Geometry Algebraic Topology 57S12, 14M25, 15B99 Motivated by a work of Fu-So-Song, we associate a symmetric matrix $A$ to a plane vector sequence $v$ and give a formula to find the signature of $A$ in terms of the sequence $v$. When $A$ is nonsingular, we interpret the relation between $A$ and $A^{-1}$ from a topological viewpoint. Finally, we associate an omnioriented quasitoric orbifold $X$ of real dimension four to the sequence $v$ and show that $A^{-1}$ is the intersection matrix of the characteristic suborbifolds of $X$. |
| title | Symmetric matrices defined by plane vector sequences |
| topic | Combinatorics Algebraic Geometry Algebraic Topology 57S12, 14M25, 15B99 |
| url | https://arxiv.org/abs/2503.06836 |