{"paper":{"title":"Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chuanning Song, Qingxiang Xu, Wei Luo","submitted_at":"2018-06-19T03:54:39Z","abstract_excerpt":"Let $\\mathbb{C}^{n\\times n}$ be the set of all $n \\times n$ complex matrices. For any Hermitian positive semi-definite matrices $A$ and $B$ in $\\mathbb{C}^{n\\times n}$, their new common upper bound less than $A+B-A:B$ is constructed, where $(A+B)^\\dag$ denotes the Moore-Penrose inverse of $A+B$, and $A:B=A(A+B)^\\dag B$ is the parallel sum of $A$ and $B$. A factorization formula for $(A+X):(B+Y)-A:B-X:Y$ is derived, where $X,Y\\in\\mathbb{C}^{n\\times n}$ are any Hermitian positive semi-definite perturbations of $A$ and $B$, respectively. Based on the derived factorization formula and the construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07033","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"}