Convexity of the dominant eigenvalue of an essentially nonnegative matrix

Cohen, Joel E.

doi:10.1090/S0002-9939-1981-0601750-2

Convexity of the dominant eigenvalue of an essentially nonnegative matrix
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Proc. Amer. Math. Soc. 81 (1981), 657-658 Request permission

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.

References

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