Submatrices with the best-bounded inverses: Studying \mathdsR^{n × 2} and \mathdsC^{n × 2}

2024/08/29 by Yuri Valentinovich Nesterenko, Nesterenko, Yuri
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2408.16631

openalex publication_date 2024/08/29 · openalex created_date 2024/09/22 · openalex updated_date 2026/07/28

Abstract

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 \citeGTZ1997, and at the same time presents a new application of the results by Hausmann and Knutson \citeHK1997.

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