{"paper":{"title":"Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Wojciech Tarnowski, Yan V. Fyodorov","submitted_at":"2019-10-21T08:36:06Z","abstract_excerpt":"We study the distribution of the eigenvalue condition numbers $\\kappa_i=\\sqrt{ (\\mathbf{l}_i^* \\mathbf{l}_i)(\\mathbf{r}_i^* \\mathbf{r}_i)}$ associated with real eigenvalues $\\lambda_i$ of partially asymmetric $N\\times N$ random matrices from the real Elliptic Gaussian ensemble. The large values of $\\kappa_i$ signal the non-orthogonality of the (bi-orthogonal) set of left $\\mathbf{l}_i$ and right $\\mathbf{r}_i$ eigenvectors and enhanced sensitivity of the associated eigenvalues against perturbations of the matrix entries. We derive the general finite $N$ expression for the joint density functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09204","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.09204/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}