{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/grassmann-and-flag-varieties-in-linear","title":"Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective","arxiv_id":"2505.15969","date":"2025-05-21","proceeding":null,"authors":["Hannah Friedman","Serkan Hoşten"],"abstract":"Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure of the algebraic complexity is the amount of complex critical points of the corresponding optimization problem. After an exposition of different realizations of these manifolds as algebraic varieties we present a sample of optimization problems over them and we compute their algebraic complexity.","url_abs":"https://arxiv.org/abs/2505.15969v1","url_pdf":"https://arxiv.org/pdf/2505.15969v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"grassmann-and-flag-varieties-in-linear","repo_url":"https://github.com/hannahfriedman/flag_optimization_algebraic_perspective","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}