Rump, Siegfried M.Siegfried M.Rump2021-05-052021-05-051998-11-02Linear Algebra and Its Applications 279 (1-3): 177-180 (1998)http://hdl.handle.net/11420/9441The extension of the Perron-Frobenius theory to real matrices without sign restriction uses the sign-real spectral radius as the generalization of the Perron root. The theory was used to extend and solve the conjecture in the affirmative that an ill-conditioned matrix is nearby a singular matrix also in the componentwise sense. The proof estimates the ratio between the sign-real spectral radius and the maximum geometric mean of a cycle product. In this note we discuss bounds for this ratio including a counterexample to a conjecture about this ratio.en0024-379519981-3177180American Elsevier Publ.Componentwise distancesPerron-Frobenius theorySign-real spectral radiusMathematikJournal Article10.1016/S0024-3795(98)00014-7Journal Article