Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices

Sahi, Siddhartha

doi:10.1090/S0002-9939-1993-1139482-5

Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices
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Proc. Amer. Math. Soc. 118 (1993), 1035-1036 Request permission

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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