Submatrices with the best-bounded inverses: Studying $\mathdsR^n \times 2$ and $\mathdsC^n \times 2$
<|reference_start|>Submatrices with the best-bounded inverses: Studying $\mathdsR^n \times 2$ and $\mathdsC^n \times 2$: 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}.<|reference_end|>
@article{nesterenko2024submatrices,
    title={Submatrices with the best-bounded inverses: Studying $\mathds{R}^{n
  \times 2}$ and $\mathds{C}^{n \times 2}$},
    author={Yuri Nesterenko},
    journal={arXiv preprint arXiv:2408.16631},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.16631},
    primaryClass={math.NA cs.NA math.DG}
}