Submatrices with the best-bounded inverses: Studying $\mathds{R}^{n \times 2}$ and $\mathds{C}^{n \times 2}$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917762258960384 |
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| author | Nesterenko, Yuri |
| author_facet | Nesterenko, Yuri |
| contents | In both real and complex cases, we establish the connection of the problem about $2$-dimensional linear subspaces the most deviating from the coordinate ones with one simply formulated optimization problem for isoperimetric polygons in Euclidean spaces.
This study thereby provides a new geometrical point of view on the $2$-dimensional case of the problem formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997}, and at the same time presents a new application of the results by Hausmann and Knutson \cite{HK1997}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Submatrices with the best-bounded inverses: Studying $\mathds{R}^{n \times 2}$ and $\mathds{C}^{n \times 2}$ Nesterenko, Yuri Numerical Analysis Differential Geometry In both real and complex cases, we establish the connection of the problem about $2$-dimensional linear subspaces the most deviating from the coordinate ones with one simply formulated optimization problem for isoperimetric polygons in Euclidean spaces. This study thereby provides a new geometrical point of view on the $2$-dimensional case of the problem formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997}, and at the same time presents a new application of the results by Hausmann and Knutson \cite{HK1997}. |
| title | Submatrices with the best-bounded inverses: Studying $\mathds{R}^{n \times 2}$ and $\mathds{C}^{n \times 2}$ |
| topic | Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2408.16631 |