A uniform type inverse spectrum theorem for entrywise nonnegative matrices (Q869903)
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scientific article; zbMATH DE number 5132601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A uniform type inverse spectrum theorem for entrywise nonnegative matrices |
scientific article; zbMATH DE number 5132601 |
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A uniform type inverse spectrum theorem for entrywise nonnegative matrices (English)
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9 March 2007
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An unordered list \(L= \{z_1,z_2,\dots, z_n\}\subset\mathbb{C}^n\) is called self-conjugate if \(L=\overline L=\{\overline z_1,\overline z_2,\dots,\overline z_n\}\). It is shown that a positive integer \(n-1\) together with any self-conjugate list of \(n-1\) complex numbers from the closed unit disk forms the spectrum of a nonnegative matrix of order \(n\), but no \(r< n-1\) has this property. Motivating papers were published earlier by \textit{M. Fiedler} [Linear Algebra Appl. 9, 119--142 (1974; Zbl 0322.15015)].
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spectrum of nonnegative matrix
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(uniform) inverse eigenvalue problem
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circulant matrix
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