Convexity and log convexity for the spectral radius (Q1073138)
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scientific article; zbMATH DE number 3944047
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity and log convexity for the spectral radius |
scientific article; zbMATH DE number 3944047 |
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Convexity and log convexity for the spectral radius (English)
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1986
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Results of \textit{J. F. C. Kingman} [Quart. J. Math., Oxford II. Ser. 12, 283-284 (1961; Zbl 0101.253)], \textit{J. E. Cohen} [Math. Proc. Camb. Philos. Soc. 86, 345-350 (1979; Zbl 0415.60012)], \textit{S. Friedland} and \textit{S. Karlin} [Duke Math. J. 42, 459-490 (1975; Zbl 0373.15008)] on convexity, log convexity and ''min-max'' characterizations of the spectral radius of a nonnegative matrix are reviewed. Generalizations of some of the results to cone spectral radii are given and a problem of population biology concerning the uniqueness of the eigenvector corresponding to the spectral radius in a cone is solved.
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Perron vector
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convexity
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log convexity
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''min-max'' characterizations
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spectral radius
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nonnegative matrix
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population biology
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