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The inverse eigenvalue problem for symmetric doubly stochastic matrices. (English) Zbl 1040.15010

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.

MSC:

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

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