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Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices

Author: Siddhartha Sahi
Journal: Proc. Amer. Math. Soc. 118 (1993), 1035-1036
MSC: Primary 15A48; Secondary 15A51
MathSciNet review: 1139482
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Abstract: Let $ C(S)$ be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix $ S$. For each $ 0 \leqslant \alpha \leqslant 1$, it is shown that if $ u$ and $ v$ are in $ C(S)$ then so is $ w$, where $ {w_j} = u_j^\alpha v_j^{1 - \alpha }$.

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Keywords: Positive matrix, stochastic matrix, Perron-Frobenius eigenvector, convexity
Article copyright: © Copyright 1993 American Mathematical Society

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