{"paper":{"title":"Submatrices with the best-bounded inverses: Studying $\\mathds{R}^{n \\times 2}$ and $\\mathds{C}^{n \\times 2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DG"],"primary_cat":"math.NA","authors_text":"Yuri Nesterenko","submitted_at":"2024-08-29T15:38:07Z","abstract_excerpt":"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.\n  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}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16631","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.16631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}