{"paper":{"title":"New perturbation bounds for the spectrum of a normal matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chen-Song Zhang, Xuefeng Xu","submitted_at":"2016-12-17T13:41:54Z","abstract_excerpt":"Let $A\\in\\mathbb{C}^{n\\times n}$ and $\\widetilde{A}\\in\\mathbb{C}^{n\\times n}$ be two normal matrices with spectra $\\{\\lambda_{i}\\}_{i=1}^{n}$ and $\\{\\widetilde{\\lambda}_{i}\\}_{i=1}^{n}$, respectively. The celebrated Hoffman--Wielandt theorem states that there exists a permutation $\\pi$ of $\\{1,\\ldots,n\\}$ such that $\\left(\\sum_{i=1}^{n}\\big|\\widetilde{\\lambda}_{\\pi(i)}-\\lambda_{i}\\big|^{2}\\right)^{1\\over 2}$ is no larger than the Frobenius norm of $\\widetilde{A}-A$. However, if either $A$ or $\\widetilde{A}$ is non-normal, this result does not hold in general. In this paper, we present several "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05759","kind":"arxiv","version":2},"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"}