A sufficient condition for the existence of an \(M\)-matrix with prescribed spectrum (Q5948844)
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scientific article; zbMATH DE number 1672083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sufficient condition for the existence of an \(M\)-matrix with prescribed spectrum |
scientific article; zbMATH DE number 1672083 |
Statements
A sufficient condition for the existence of an \(M\)-matrix with prescribed spectrum (English)
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12 November 2001
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The inverse spectrum problem for \(M\)-matrices is studied. This problem involves finding necessary and sufficient conditions for an \(n\)-tuple of complex numbers to be the spectrum of an \(n\times n\) \(M\)-matrix. A sufficient condition is determined for the existence of \(M\)-matrices of low order with a prescribed spectrum. Then these results are combined to obtain a sufficient condition for an \(M\)-matrix of order \(n\). Finally a sufficient condition is found for the existence of a nonnegative matrix with prescribed complex spectrum.
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\(M\)-matrices
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inverse spectrum problem
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nonnegative matrix
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prescribed complex spectrum
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