{"paper":{"title":"On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Aaron Welters","submitted_at":"2009-05-25T17:40:11Z","abstract_excerpt":"Let A(z) be an analytic square matrix and $\\lambda_{0}$ an eigenvalue of A(0) of multiplicity m. Then under the generic condition, the characteristic polynomial of A(z) evaluated at $\\lambda_{0}$ has a simple zero at z=0, we prove that the Jordan normal form of A(0) corresponding to the eigenvalue $\\lambda_{0}$ consists of a single m-by-m Jordan block, the perturbed eigenvalues near $\\lambda_{0}$ and their eigenvectors can be represented by a single convergent Puiseux series containing only powers of z^{1/m}, and there are explicit recursive formulas to compute all the Puiseux series coefficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4051","kind":"arxiv","version":3},"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"}