Kaddoura, I.; Mourad, B. On a conjecture concerning the inverse eigenvalue problem of \(4 \times 4\) symmetric doubly stochastic matrices. (English) Zbl 1166.15004 Int. Math. Forum 3, No. 29-32, 1513-1519 (2008). The authors give a counter example of the second named author’s conjecture 3. 11 in [Linear Algebra Appl. 416, No. 2–3, 546–558 (2006; Zbl 1101.15023)], about a characterization of the spectrum \((1,x,y,z)\) of \(4\times 4\) symmetric stochastic matrices with \(1\geq x\geq y\geq z\geq -1\). In addition, a new featured subset of the region where the decreasingly ordered spectra of \(4\times 4\) symmetric doubly stochastic matrices lie is found. Reviewer: Huang Wenxue (Scarborough) Cited in 4 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra 15B51 Stochastic matrices Keywords:doubly stochastic matrices; inverse eigenvalue problem; spectra of matrices; symmetric doubly stochastic matrices Citations:Zbl 1101.15023 PDFBibTeX XMLCite \textit{I. Kaddoura} and \textit{B. Mourad}, Int. Math. Forum 3, No. 29--32, 1513--1519 (2008; Zbl 1166.15004) Full Text: Link