{"paper":{"title":"Products of orthogonal projections and polar decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandra Maestripieri, Gustavo Corach","submitted_at":"2010-11-23T21:21:25Z","abstract_excerpt":"We characterize the sets $\\XX$ of all products $PQ$, and $\\YY$ of all products $PQP$, where $P,Q$ run over all orthogonal projections and we solve the problems $\\arg\\min\\{\\|P-Q\\|: (P,Q) \\in \\cal Z\\}$, for $\\cal Z=\\XX$ or $\\YY.$ We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of $\\XX.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5237","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":""},"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"}