{"paper":{"title":"Projections and Idempotents in star-reducing Rings Involving the Moore-Penrose Inverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Long Wang, Shuangshuang Zhang, Xiaoxiang Zhang","submitted_at":"2013-07-21T14:15:47Z","abstract_excerpt":"In [Comput. Math. Appl. 59 (2010) 764-778], Baksalary and Trenkler characterized some complex idempotent matrices of the form $(I-PQ)^{\\dag}P(I-Q)$, $(I-QP)^{\\dag}(I-Q)$ and $P(P+Q-QP)^{\\dag}$ in terms of the column spaces and null spaces of $P$ and $Q$, where $P, Q\\in \\mathbb{C}^{\\textsf{OP}}_n = \\{L\\in \\mathbb{C}_{n,n}\\ |\\ L^2 = L = L^*\\}$. We generalize these results from $\\mathbb{C}_{n,n}$ to any *-reducing rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5528","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"}