{"paper":{"title":"Distributions of Demmel and Related Condition Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Matthew McKay, Prathapasinghe Dharmawansa, Yang Chen","submitted_at":"2012-11-02T18:38:29Z","abstract_excerpt":"Consider a random matrix $\\mathbf{A}\\in\\mathbb{C}^{m\\times n}$ ($m \\geq n$) containing independent complex Gaussian entries with zero mean and unit variance, and let $0<\\lambda_1\\leq \\lambda_{2}\\leq ...\\leq \\lambda_n<\\infty$ denote the eigenvalues of $\\mathbf{A}^{*}\\mathbf{A}$ where $(\\cdot)^*$ represents conjugate-transpose. This paper investigates the distribution of the random variables $\\frac{\\sum_{j=1}^n \\lambda_j}{\\lambda_k}$, for $k = 1$ and $k = 2$. These two variables are related to certain condition number metrics, including the so-called Demmel condition number, which have been show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0517","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"}