Fang, Maozhong A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices. (English) Zbl 1193.15009 Linear Algebra Appl. 432, No. 11, 2925-2927 (2010). S.-G. Hwang and S.-S. Pyo [ibid. 379, 77–83 (2004; Zbl 1040.15010)] had claimed as a proposition that a real \(n\)-tuple \(1\geq \lambda_2 \geq \cdots \geq \lambda_n\) such that \[ \frac{1}{n} +\frac{\lambda_2}{n(n-1)}+\frac{\lambda_3}{(n-1)(n-2)}+\ldots +\frac{\lambda_n}{2(1)}\geq 0 \]is the spectrum of a symmetric doubly stochastic matrix. In this note, the author points out by a counterexample that the proposition is wrong. Reviewer: Huang Wenxue (Scarborough) Cited in 1 ReviewCited in 6 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra 15B51 Stochastic matrices Keywords:symmetric doubly stochastic matrices; inverse eigenvalue problem; spectrum; counterexample Citations:Zbl 1040.15010 PDFBibTeX XMLCite \textit{M. Fang}, Linear Algebra Appl. 432, No. 11, 2925--2927 (2010; Zbl 1193.15009) Full Text: DOI References: [1] Horn, R. A.; Johnson, C. R., Matrix Analysis (1985), Cambridge University Press · Zbl 0576.15001 [2] Hwang, S. G.; Pyo, S. S., The inverse eigenvalue problem for symmetric doubly stochastic matrices, Linear Algebra Appl., 379, 77-83 (2004) · Zbl 1040.15010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.