A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices (Q967507)
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scientific article; zbMATH DE number 5702831
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices |
scientific article; zbMATH DE number 5702831 |
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A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices (English)
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29 April 2010
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\textit{S.-G. Hwang} and \textit{S.-S. Pyo} [ibid. 379, 77--83 (2004; Zbl 1040.15010)] had claimed as a proposition 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. In this note, the author points out by a counterexample that the proposition is wrong.
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symmetric doubly stochastic matrices
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inverse eigenvalue problem
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spectrum
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counterexample
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