Hwang, Suk-Geun; Pyo, Sung-Soo The inverse eigenvalue problem for symmetric doubly stochastic matrices. (English) Zbl 1040.15010 Linear Algebra Appl. 379, 77-83 (2004). The authors study the possible spectra of symmetric doubly stochastic and related matrices. It is proved 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. Reviewer: Ki Hang Kim (Montgomery) Cited in 1 ReviewCited in 20 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra 15B51 Stochastic matrices Keywords:inverse eigenvalue problem; spectrum; doubly stochastic matrix PDFBibTeX XMLCite \textit{S.-G. Hwang} and \textit{S.-S. Pyo}, Linear Algebra Appl. 379, 77--83 (2004; Zbl 1040.15010) Full Text: DOI References: [1] Borobia, A., On the nonnegative eigenvalue problem, Linear Algebra Appl., 223/224, 131-140 (1995) · Zbl 0831.15014 [2] Fiedler, M., Eigenvalues of nonnegative symmetric matrices, Linear Algebra Appl., 9, 119-142 (1974) · Zbl 0322.15015 [3] Horn, R.; Johnson, C., Matrix Analysis (1985), Cambridge University Press · Zbl 0576.15001 [4] Kellog, R. B., Matrices similar to a positive or essentially positive matix, Linear Algebra Appl., 4, 191-204 (1971) · Zbl 0215.37504 [5] Salzmann, F. L., A note on eigenvalues of nonnegative matrices, Linear Algebra Appl., 5, 329-338 (1972) · Zbl 0255.15009 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.