On the nonnegative eigenvalue problem

Dedicated to M. Fiedler and V. Pták
https://doi.org/10.1016/0024-3795(94)00343-CGet rights and content
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Abstract

{1, λ1, …, λn} is the spectrum of a stochastic matrix of order n + 1 if and only if there exists some real matrix B of order n with spectrum {λ1, …, λn} and some n-simplex SRn containing the origin such that BSS. This result appears implicitly in Ciarlet's work, and it provides us with a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem. We employ it here to generalize the sufficient conditions given by Kellogg.

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Partially supported by DGICYT PB92-0716.