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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convexity of the dominant eigenvalue of an essentially nonnegative matrix


Author: Joel E. Cohen
Journal: Proc. Amer. Math. Soc. 81 (1981), 657-658
MSC: Primary 15A42; Secondary 15A48, 92A15
MathSciNet review: 601750
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Abstract: The dominant eigenvalue of a real $ n \times n$ matrix $ A$ with nonnegative elements off the main diagonal is a convex function of the diagonal of $ A$. We give a short proof using Trotter's product formula and a theorem on log-convexity due to Kingman.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0601750-2
PII: S 0002-9939(1981)0601750-2
Keywords: Perron-Frobenius root, convexity, log-convexity, Trotter product formula, spectral radius
Article copyright: © Copyright 1981 American Mathematical Society