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On a conjecture concerning the inverse eigenvalue problem of \(4 \times 4\) symmetric doubly stochastic matrices. (English) Zbl 1166.15004

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.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A29 Inverse problems in linear algebra
15B51 Stochastic matrices

Citations:

Zbl 1101.15023
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