The inverse eigenvalue problem for symmetric doubly stochastic matrices.
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.
scientific article; zbMATH DE number 2056678