Localization of Perron roots (Q1887498)
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scientific article; zbMATH DE number 2119131
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Localization of Perron roots |
scientific article; zbMATH DE number 2119131 |
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Localization of Perron roots (English)
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26 November 2004
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The localization of the Perron root of a nonnegative irreducible matrix is discussed. Recall the spectral radius of a complex matrix \(A\) is defined as the maximum of absolute values of its eigenvalues. It is known that if a real matrix is irreducible and nonnegative then its spectral radius is its eigenvalue (the Perron root). A new localization method giving relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complements is given. Some numerical examples are presented.
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Nonnegative irreducible matrix
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Perron complement
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Perron root
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Spectral radius
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eigenvalue
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numerical examples
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